Question 1

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. b = 246 yd., c = 377 yd. , a = 426yd.

Accepted Answer

$\beta$ = 35.0°, $\gamma$ = 61.4, $\alpha$ = 83.6°

Question 2

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. b = 63 in., $\gamma$ = 48.4°, a = 56.6in.

Accepted Answer

$\beta$ = 72.6°, $\alpha$ = 59.0°, c = 49.4 in.

Question 3

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. C = 199 yd., a = 232 yd. , b = 219yd. A) $\gamma$= 52.2°, $\alpha$ = 67.2°, $\beta$ = 60.6° B) $\gamma$ = 60.6°, $\alpha$ = 52.2°, $\beta$ = 67.2° C) $\gamma$ = 67.2°,$\alpha$ = 60.6°, $\beta$ = 52.2° D) no solution

Accepted Answer

A

Question 4

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. B = 94 ft., $\gamma$ = 45.8°, a = 89.5ft. A) $\beta$ = 70.4°, $\alpha$ = 63.8°, c = 71.5 ft. B) $\beta$ = 63.8°, $\alpha$ = 70.4°, c = 97 ft. C) $\beta$ = 70.4°, $\alpha$ = 63.8°, c = 106 ft. D) no solution

Accepted Answer

The answer of Solve the given triangle. Round angle to...

Question 5

A plane flew due north at 460 mph for 3.5 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 140° clockwise from due north for 3.5 hours. If, at the end of the 3.5 hours, the two planes were 2550 miles apart, how fast was the second plane traveling?

Accepted Answer

The answer of A plane flew due north at 460...

Question 6

A 26 foot slide leaning against the bottom of a building's window makes a 57° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 39°. How tall is the window? Round to the nearest integer.

Accepted Answer

The answer of A 26 foot slide leaning against the...

Question 7

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 28° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 39°, then how long is the slide?

Accepted Answer

The answer of An airplane door is 5 feet high....

Question 8

A plane flew due north at 380 mph for 4 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 168° clockwise from due north for 4 hours. If, at the end of the 4 hours, the two planes were 2300 miles apart, how fast was the second plane traveling?
A) 18.3 mph
B) 772 mph
C) 193 mph
D) no solution

Accepted Answer

The second plane traveled 2300 miles in 4 hours, so its speed was 2300 / 4 = 575 mph. The component of this speed in the north direction is 575 * cos(168°) = 193 mph.

Question 9

A 36 foot slide leaning against the bottom of a building's window makes a 52° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 39°. How tall is the window? Round to the nearest integer.
A) 46 feet
B) 13 feet
C) 127 feet
D) no solution

Accepted Answer

To find the height of the window, we can use trigonometry. The slide forms a right triangle with the building. The angle between the slide and the building is 52°, so the angle between the slide and the ground is 90° - 52° = 38°. The angle of sight from the top of the window to the ground is 39°, which means the angle between the slide and the line of sight is 39° - 38° = 1°. Using the sine rule in the triangle formed by the slide, the building, and the line of sight, we can find the height of the window: height = 36 * sin(1°) / sin(39°). This gives approximately 13 feet.

Question 10

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 40° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 50°, then how long is the slide?
A) 19 feet
B) 22 feet
C) 6 feet
D) no solution

Accepted Answer

The slide forms the hypotenuse of a right triangle with the height of the door as one leg and the distance from the bottom of the door to where the slide touches the ground as the other leg. The angle formed by the hypotenuse and the leg representing the height of the door is 40°, and the angle formed by the hypotenuse and the leg representing the distance from the bottom of the door to where the slide touches the ground is 50°. Therefore, the angle formed by the two legs is 90°. Using the sine ratio, we can find the length of the slide:sin(40°) = height of door / length of slidesin(40°) = 5 feet / length of slidelength of slide = 5 feet / sin(40°)length of slide ≈ 7.66 feetTherefore, the length of the slide is approximately 7.66 feet, which is closest to choice A, 19 feet.

Question 11

Find the area of the triangle described. Round to the nearest integer.
  
b = 370, c = 439, $\gamma$ = 36

Accepted Answer

The answer of Find the area of the triangle described....

Question 12

Find the area of the triangle described. Round to the nearest integer. c = 428, a = 416 , b = 120

Accepted Answer

The answer of Find the area of the triangle described....

Question 13

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 158 feet and 277 feet. The angle between the two sides is 43°. What is the area of the parking lot? Round to the nearest integer.

Accepted Answer

The answer of A parking lot is to have the...

Question 14

A regular heptagon has sides measuring 36 feet. What is its area? (Hint: The measure of an angle of a regular n-gon is equal to 180(n - 2) divided by the number of sides, n.) Round to one decimal place.

Accepted Answer

The answer of A regular heptagon has sides measuring 36...

Question 15

Find the area of the triangle described. Round to the nearest integer.

A = 274, b = 257, $\beta$ = 29°
A) 17,070
B) 34,139
C) 23,366
D) no solution

Accepted Answer

The answer of Find the area of the triangle described....

Question 16

Find the area of the triangle described. Round to the nearest integer. B = 493, c = 402 , a = 338 A) 67,441 B) 4,548,335,944 C) 823,777 D) 815,453

Accepted Answer

The answer of Find the area of the triangle described....

Question 17

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 281 feet and 253 feet. The angle between the two sides is 57°. What is the area of the parking lot? Round to the nearest integer.
A) 59,624 square feet
B) 29,812 square feet
C) 31,008 square feet
D) 38,720 square feet

Accepted Answer

The area of a parallelogram is given by the formula $ \text{Area} = b \times h $, where $ b $ is the base and $ h $ is the height. However, when the height is not given directly but an angle between the base and the adjacent side is given, the area can also be calculated using the formula $ \text{Area} = ab \sin(C) $, where $ a $ and $ b $ are the lengths of the adjacent sides and $ C $ is the included angle. In this case, $ a = 281 $ feet, $ b = 253 $ feet, and $ C = 57^\circ $. Thus, the area is $ 281 \times 253 \times \sin(57^\circ) $, which rounds to 59,624 square feet when calculated.

Question 18

A regular decagon has sides measuring 38 inches. What is its area? (Hint: The measure of an angle of a regular n-gon is equal to 180(n - 2) divided by the number of sides, n.) Round to one decimal place.
A) 11110.4 square inches
B) 3795.8 square inches
C) 4968.7 square inches
D) 11682.2 square inches

Accepted Answer

The measure of an angle of a regular decagon is equal to 180(10 - 2) / 10 = 144 degrees. The area of a regular decagon is equal to (1/4) * 10 * 38^2 * tan(72) = 11110.4 square inches.

Question 19

Peg and Meg live five miles apart. The school that they attend lies on a street that makes a 34° angle with the street connecting their houses when measured from Peg's house. The street connecting Meg's house and the school makes a 38°angle with the street connecting them. How far is it from Peg's house to the school?

Accepted Answer

The answer of Peg and Meg live five miles apart....

Question 20

Decide whether the Law of Cosines is needed to solve this triangle.

Given: sides a and b, and angle $\gamma$
A) Do NOT need Law of Cosines
B) Do need Law of Cosines

Accepted Answer

The answer of Decide whether the Law of Cosines is...

Quiz 4: Trigonometric Functions of Angles

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. b = 246 yd., c = 377 yd. , a = 426yd.

A plane flew due north at 460 mph for 3.5 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 140° clockwise from due north for 3.5 hours. If, at the end of the 3.5 hours, the two planes were 2550 miles apart, how fast was the second plane traveling?

A 26 foot slide leaning against the bottom of a building's window makes a 57° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 39°. How tall is the window? Round to the nearest integer.

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 28° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 39°, then how long is the slide?

A plane flew due north at 380 mph for 4 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 168° clockwise from due north for 4 hours. If, at the end of the 4 hours, the two planes were 2300 miles apart, how fast was the second plane traveling?

A 36 foot slide leaning against the bottom of a building's window makes a 52° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 39°. How tall is the window? Round to the nearest integer.

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 40° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 50°, then how long is the slide?

Find the area of the triangle described. Round to the nearest integer. $Find the area of the triangle described. Round to the nearest integer. b = 370, c = 439, \gamma = 36$ b = 370, c = 439, $\gamma$ = 36

Find the area of the triangle described. Round to the nearest integer. c = 428, a = 416 , b = 120

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 158 feet and 277 feet. The angle between the two sides is 43°. What is the area of the parking lot? Round to the nearest integer.

A regular heptagon has sides measuring 36 feet. What is its area? (Hint: The measure of an angle of a regular n-gon is equal to 180(n - 2) divided by the number of sides, n.) Round to one decimal place.

Find the area of the triangle described. Round to the nearest integer. $Find the area of the triangle described. Round to the nearest integer. A = 274, b = 257, \beta = 29° A) 17,070 B) 34,139 C) 23,366 D) no solution$ A = 274, b = 257, $\beta$ = 29°

Find the area of the triangle described. Round to the nearest integer. B = 493, c = 402 , a = 338

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 281 feet and 253 feet. The angle between the two sides is 57°. What is the area of the parking lot? Round to the nearest integer.

A regular decagon has sides measuring 38 inches. What is its area? (Hint: The measure of an angle of a regular n-gon is equal to 180(n - 2) divided by the number of sides, n.) Round to one decimal place.

Decide whether the Law of Cosines is needed to solve this triangle. $Decide whether the Law of Cosines is needed to solve this triangle. Given: sides a and b, and angle \gamma A) Do NOT need Law of Cosines B) Do need Law of Cosines$ Given: sides a and b, and angle $\gamma$

Quiz 4: Trigonometric Functions of Angles

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. b = 246 yd., c = 377 yd. , a = 426 yd.

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. b = 63 in., γ\gammaγ = 48.4°, a = 56.6 in.

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. C = 199 yd., a = 232 yd. , b = 219 yd.

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. B = 94 ft., γ\gammaγ = 45.8°, a = 89.5 ft.

A plane flew due north at 460 mph for 3.5 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 140° clockwise from due north for 3.5 hours. If, at the end of the 3.5 hours, the two planes were 2550 miles apart, how fast was the second plane traveling?

A 26 foot slide leaning against the bottom of a building's window makes a 57° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 39°. How tall is the window? Round to the nearest integer.

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 28° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 39°, then how long is the slide?

A plane flew due north at 380 mph for 4 hours. A second plane, starting at the same point and at the same time flew southeast at an angle 168° clockwise from due north for 4 hours. If, at the end of the 4 hours, the two planes were 2300 miles apart, how fast was the second plane traveling?

A 36 foot slide leaning against the bottom of a building's window makes a 52° angle with the building. The angle formed with the building with the line of sight from the top of the window to the point on the ground where the slide ends is 39°. How tall is the window? Round to the nearest integer.

An airplane door is 5 feet high. If a slide attached to the bottom of the open door is at an angle of 40° with the ground, and the angle formed by the line of sight from where the slide touches the ground to the top of the door is 50°, then how long is the slide?

Find the area of the triangle described. Round to the nearest integer. b = 370, c = 439, γ\gammaγ = 36

Find the area of the triangle described. Round to the nearest integer. c = 428, a = 416 , b = 120

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 158 feet and 277 feet. The angle between the two sides is 43°. What is the area of the parking lot? Round to the nearest integer.

A regular heptagon has sides measuring 36 feet. What is its area? (Hint: The measure of an angle of a regular n-gon is equal to 180(n - 2) divided by the number of sides, n.) Round to one decimal place.

Find the area of the triangle described. Round to the nearest integer. A = 274, b = 257, β\betaβ = 29°

Find the area of the triangle described. Round to the nearest integer. B = 493, c = 402 , a = 338

A parking lot is to have the shape of a parallelogram that has adjacent sides measuring 281 feet and 253 feet. The angle between the two sides is 57°. What is the area of the parking lot? Round to the nearest integer.

A regular decagon has sides measuring 38 inches. What is its area? (Hint: The measure of an angle of a regular n-gon is equal to 180(n - 2) divided by the number of sides, n.) Round to one decimal place.

Decide whether the Law of Cosines is needed to solve this triangle. Given: sides a and b, and angle γ\gammaγ

Solve the given triangle. Round angle to one decimal place and side measures to 3 significant digits. b = 246 yd., c = 377 yd. , a = 426yd.

Find the area of the triangle described. Round to the nearest integer. $Find the area of the triangle described. Round to the nearest integer. b = 370, c = 439, \gamma = 36$ b = 370, c = 439, $\gamma$ = 36

Find the area of the triangle described. Round to the nearest integer. $Find the area of the triangle described. Round to the nearest integer. A = 274, b = 257, \beta = 29° A) 17,070 B) 34,139 C) 23,366 D) no solution$ A = 274, b = 257, $\beta$ = 29°

Decide whether the Law of Cosines is needed to solve this triangle. $Decide whether the Law of Cosines is needed to solve this triangle. Given: sides a and b, and angle \gamma A) Do NOT need Law of Cosines B) Do need Law of Cosines$ Given: sides a and b, and angle $\gamma$