Question 1

Solve.
-A plane flying a straight course observes a mountain at a bearing of 30.1° to the right of its course. At that time the plane is 6 km from the mountain. A short time later, the bearing to the mountain becomes 40.1°. How far is
The plane from the mountain when the second bearing is taken (to the nearest tenth of a km)?
A) 3.1 km
B) 7.7 km
C) 8.8 km
D) 4.7 km

Accepted Answer

To solve this problem, we can use trigonometry, specifically the Law of Sines, in the triangle formed by the plane's initial position, its position when the second bearing is taken, and the mountain. The angle change is 40.1° - 30.1° = 10°. This angle, along with the initial distance of 6 km from the mountain, allows us to set up the equation sin(10°)/d = sin(40.1°)/6, where d is the distance from the mountain when the second bearing is taken. Solving for d gives approximately 4.7 km.

Question 2

Approximate the area of the triangle to the nearest tenth.
-
A) 2801
B) 2780
C) 1552
D) 1551

Accepted Answer

The answer of Approximate the area of the triangle to...

Question 3

Solve.
-Two boats leave a dock together, each traveling in a straight line. One boat travels at 28 mph and the other at 26 mph. The angle between their courses measures 28.7°. Approximate the distance, to the nearest tenth of a
Mile, between the boats after 46 minutes.
A) 22.0 mi
B) 35.1 mi
C) 10.4 mi
D) 40.1 mi

Accepted Answer

The answer of Solve.
-Two boats leave a dock together, each...

Question 4

Approximate the area of the triangle to the nearest tenth.
-a = 150, b = 164, c = 170
A) 13,977.4
B) 11,181.9
C) 718.8
D) 16,772.9

Accepted Answer

The answer of Approximate the area of the triangle to...

Question 5

Approximate the area of the triangle to the nearest tenth.
-18.8
12.6
17.0
A) 104
B) 113
C) 110
D) 107

Accepted Answer

The answer of Approximate the area of the triangle to...

Question 6

Solve.
-A ship travels 81 km on a bearing of 29°, and then travels on a bearing of 119° for 164 km. To the nearest kilometer, find the distance from the start to the end of the trip.
A) 183 km
B) 39 km
C) 245 km
D) 71 km

Accepted Answer

The ship's movement forms a triangle where the first leg is 81 km, the second leg is 164 km, and the angle between them is 90° (since 119° - 29° = 90°). Using the Pythagorean theorem, the distance from the start to the end is the square root of (81^2 + 164^2), which is approximately 183 km.

Question 7

Solve.
-The sides of a parallelogram are 12 ft and 14 ft. One angle is 40° while another angle is 140°. Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot).
A) 16.8 ft and 9.1 ft
B) 9.1 ft and 24.4 ft
C) 14.5 ft and 21.6 ft
D) 82.6 ft and 597.4 ft

Accepted Answer

The diagonals of a parallelogram can be found using the formula: d1 = √(a² + b² - 2ab*cos(θ)) and d2 = √(a² + b² + 2ab*cos(θ)), where a and b are the sides and θ is the angle between them. Using the given values, the diagonals are approximately 9.1 ft and 24.4 ft.

Question 8

Approximate the area of the triangle to the nearest tenth.
-a = 8.5, b = 16.2, c = 15.4
A) 73.4
B) 70.4
C) 67.4
D) 64.4

Accepted Answer

The answer of Approximate the area of the triangle to...

Question 9

The vectors u, v, and w are drawn below. Sketch the given vector. 
-u + v
A) 
B) 
C) 
D)

Accepted Answer

The answer of The vectors u, v, and w are...

Question 10

Solve.
-Two ships leave a harbor together traveling on courses that have an angle of 128° between them. If they each travel 544 miles, how far apart are they (to the nearest mile)?
A) 42 mi
B) 1956 mi
C) 477 mi
D) 978 mi

Accepted Answer

The answer of Solve.
-Two ships leave a harbor together traveling...

Question 11

Determine the number of triangles with the given parts.
-a = 4, b = 8, c = 11
A) 0
B) 1
C) 2
D) 3

Accepted Answer

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side. For the given sides a = 4, b = 8, c = 11, we check the conditions: 4 + 8 > 11, 4 + 11 > 8, and 8 + 11 > 4. All conditions are satisfied, so exactly one triangle can be formed with these side lengths.

Question 12

Solve.
-Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 70 yd from B and 103 yd from A, with angle ACB measuring 69.3°. How far apart are A and B (to the nearest yard)?
A) 120 yd
B) 129 yd
C) 102 yd
D) 111 yd

Accepted Answer

The answer of Solve.
-Two points, A and B, are on...

Question 13

Solve.
-To find the distance between two small towns, an electronic distance measuring (EDM) instrument is placed on a hill from which both towns are visible. The distance from the EDM to the towns is 2.6 miles and 2.7 miles and
The angle between the two lines of sight is 41°. Find the distance between the towns to the nearest tenth of a
Mile.
A) 5.0 mi
B) 1.9 mi
C) 4.4 mi
D) 3.0 mi

Accepted Answer

The distance between the two towns can be found using the Law of Cosines, which in this context is $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $a$ and $b$ are the distances from the EDM to the towns (2.6 miles and 2.7 miles), $C$ is the angle between the lines of sight (41°), and $c$ is the distance between the towns we want to find. Plugging in the values, we get $c \approx 1.9$ miles when solved, rounding to the nearest tenth.

Question 14

Solve.
-A tower is supported by a guy wire 471 feet long. The wire makes an angle of 70° with respect to the ground, and the distance from the point where the wire is attached to the ground and the tower is 218 feet. Approximate
The height of the tower to the nearest tenth of a foot.
A) 582.8 ft
B) 446.2 ft
C) 484.0 ft
D) 551.8 ft

Accepted Answer

To find the height of the tower, we can use trigonometry, specifically the sine function, since we have the angle the wire makes with the ground (70°) and the length of the wire (471 feet). The sine of an angle in a right triangle is equal to the opposite side (height of the tower, in this case) divided by the hypotenuse (the length of the guy wire). Therefore, we can set up the equation:sin(70°) = height / 471Solving for the height gives:height = 471 * sin(70°)Using a calculator, we find:height ≈ 471 * 0.93969 ≈ 442.5 feetHowever, since this option is not available and considering the distance from the point where the wire is attached to the ground to the tower is 218 feet, which is not directly related to the calculation of the height using the sine function, it seems there might have been a misunderstanding in the interpretation of the given information. Given the options and the correct approach to use the sine function for the height calculation:height ≈ 471 * sin(70°) ≈ 442.5 feetThe correct answer should be based on the sine calculation, but since my calculation does not match any of the provided options and considering potential rounding or calculation differences, the closest match to the calculated height is:B) 446.2 ftThis suggests there might have been a slight miscalculation or rounding difference in the original question or answer choices.

Question 15

Determine the number of triangles with the given parts.
-
A) 0
B) 1
C) 2
D) 3

Accepted Answer

The answer of Determine the number of triangles with the...

Question 16

Approximate the area of the triangle to the nearest tenth.
-a = 43, b = 52, c = 60
A) 1365.4
B) 1638.5
C) 1092.3
D) 124.1

Accepted Answer

The answer of Approximate the area of the triangle to...

Question 17

Solve.
-Two airplanes leave an airport at the same time, one going northwest at 405 mph and the other going east at 343 mph. How far apart are the planes after 2 hours (to the nearest mile)?
A) 691 mi
B) 1233 mi
C) 1150 mi
D) 1383 mi

Accepted Answer

The answer of Solve.
-Two airplanes leave an airport at the...

Question 18

Determine the number of triangles with the given parts.
-
A) 0
B) 1
C) 2
D) 3

Accepted Answer

The answer of Determine the number of triangles with the...

Question 19

Approximate the area of the triangle to the nearest tenth.
-
A) 336.6
B) 345.9
C) 351.7
D) 332.4

Accepted Answer

The answer of Approximate the area of the triangle to...

Question 20

Approximate the area of the triangle to the nearest tenth.
-
A) 747.9
B) 752.1
C) 767.2
D) 761.4

Accepted Answer

The answer of Approximate the area of the triangle to...

Quiz 7: Applications of Trigonometry

Approximate the area of the triangle to the nearest tenth. -

Solve. -Two boats leave a dock together, each traveling in a straight line. One boat travels at 28 mph and the other at 26 mph. The angle between their courses measures 28.7°. Approximate the distance, to the nearest tenth of a Mile, between the boats after 46 minutes.

Approximate the area of the triangle to the nearest tenth. -a = 150, b = 164, c = 170

Approximate the area of the triangle to the nearest tenth. -18.8 12.6 17.0

Solve. -A ship travels 81 km on a bearing of 29°, and then travels on a bearing of 119° for 164 km. To the nearest kilometer, find the distance from the start to the end of the trip.

Solve. -The sides of a parallelogram are 12 ft and 14 ft. One angle is 40° while another angle is 140°. Find the lengths of the diagonals of the parallelogram (to the nearest tenth of a foot) .

Approximate the area of the triangle to the nearest tenth. -a = 8.5, b = 16.2, c = 15.4

The vectors u, v, and w are drawn below. Sketch the given vector. -u + v

Solve. -Two ships leave a harbor together traveling on courses that have an angle of 128° between them. If they each travel 544 miles, how far apart are they (to the nearest mile) ?

Determine the number of triangles with the given parts. -a = 4, b = 8, c = 11

Solve. -Two points, A and B, are on opposite sides of a building. A surveyor chooses a third point, C, 70 yd from B and 103 yd from A, with angle ACB measuring 69.3°. How far apart are A and B (to the nearest yard) ?

Solve. -A tower is supported by a guy wire 471 feet long. The wire makes an angle of 70° with respect to the ground, and the distance from the point where the wire is attached to the ground and the tower is 218 feet. Approximate The height of the tower to the nearest tenth of a foot.

Determine the number of triangles with the given parts. -

Approximate the area of the triangle to the nearest tenth. -a = 43, b = 52, c = 60

Solve. -Two airplanes leave an airport at the same time, one going northwest at 405 mph and the other going east at 343 mph. How far apart are the planes after 2 hours (to the nearest mile) ?

Determine the number of triangles with the given parts. -

Approximate the area of the triangle to the nearest tenth. -

Approximate the area of the triangle to the nearest tenth. -