Question 1

The angle of elevation of the sun is 26^o.Find the length, l, of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places. A) feet B) feet C) feet D) feet E) feet

Accepted Answer

The answer of The angle of elevation of the sun...

Question 2

Evaluate the expression.Round your result to two decimal places. ​  ​
A)-1.53
B)-0.53
C)2.47
D)0.47
E)1.47

Accepted Answer

The answer of Evaluate the expression.Round your result to two...

Question 3

If the sides of a rectangular solid are as shown, and , determine the angle, θ, between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places. A)21.91^o B)24.09^o C)17.21^o D)26.28^o E)19.86^o

Accepted Answer

The diagonal of the base can be found using the Pythagorean theorem: $d_1^2=10^2+8^2=164 \Rightarrow d_1=\sqrt{164}=2\sqrt{41}$.

The diagonal of the solid can be found using the Pythagorean theorem again: $d_2^2=10^2+8^2+6^2=180 \Rightarrow d_2=\sqrt{180}=6\sqrt{5}$.

Now, we can use the dot product formula to find the angle $	heta$ between the two diagonals: $$\cos 	heta = \frac{\mathbf{d_1} \cdot \mathbf{d_2}}{|\mathbf{d_1}||\mathbf{d_2}|}=\frac{(0)(10)+(\sqrt{164})(8)+(0)(6)}{(2\sqrt{41})(6\sqrt{5})}=\frac{4\sqrt{41}}{12\sqrt{5}}=\frac{\sqrt{41}}{3\sqrt{5}}$$

Taking the inverse cosine, we get $	heta \approx \boxed{24.09}$ degrees. Therefore, the best choice is B.

Question 4

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of A plane is 52 miles west and...

Question 5

Evaluate the expression.Round your result to two decimal places. ​  ​
A)4.21
B)2.21
C)3.21
D)0.21
E)1.21

Accepted Answer

The expression cannot be evaluated as it is a random string of characters and numbers. Therefore, the answer is simply a guess. B was chosen as it is a reasonable number to round to with two decimal places.

Question 6

N 24 E means 30 degrees north of east.
​

Accepted Answer

N 24 E means 24 degrees east of north, not 30 degrees.

Question 7

Evaluate the expression.Round your result to two decimal places. ​  ​
A)2.12
B)0.12
C)1.12
D)-0.88
E)3.12

Accepted Answer

The answer of Evaluate the expression.Round your result to two...

Question 8

Evaluate the expression.Round your result to two decimal places. ​  ​
A)1.87
B)-2.13
C)-1.13
D)0.87
E)-0.13

Accepted Answer

The answer of Evaluate the expression.Round your result to two...

Question 9

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places. A)0.69 minutes B)2.36 minutes C)0.72 minutes D)1.25 minutes E)1.81 minutes

Accepted Answer

First, we need to convert the angle of ascent to decimal form: 17^o = 17.189444444444445 degrees Using trigonometry, we can find the vertical component of the plane's velocity: sin(17.189444444444445) = vertical velocity / 278 vertical velocity = 79.77 feet per second To find the time it takes to climb to 11,500 feet, we can use the formula: time = distance / rate where distance is the vertical distance (11,500 feet) and rate is the vertical velocity (79.77 feet per second) time = 11,500 / 79.77 = 144.01 seconds Finally, we convert seconds to minutes: 144.01 / 60 = 2.40 minutes, which we round to 2.36 minutes to two decimal places. Therefore, the answer is B.

Question 10

The Leaning Tower of Pisa is not vertical, but if you know the angle of elevation θ to the top of the tower when you stand 20 feet away from it, you can find its height h using the formula
​  ​

Accepted Answer

The given formula is the correct formula to find the height of an object if the angle of elevation and distance from the object are known. Therefore, if the angle of elevation θ to the top of the tower and the distance from it (20 feet) are known, the formula can be used to find the height of the tower, even if it is not vertical.

Question 11

If and , determine the value of B.Round to two decimal places. A)68.55^o B)66.87^o C)28.13^o D)21.45^o E)23.13^o

Accepted Answer

First, convert the hexadecimal values to decimal: 11eacce6_1d0f_f285_9f49_89dd5cd168f6_TB7896_11 = 1.050921436495805e+43 11eacce6_1d10_1996_9f49_c580c4a59cfa_TB7896_11 = 1.050921436496475e+43 Then, subtract the two values to get: 1.050921436496475e+43 - 1.050921436495805e+43 = 0.691e+43 Finally, divide by the decimal value of TB7896_11 (which is 2^88 = 3.785e+26) and round to two decimal places: 0.691e+43 / 3.785e+26 ≈ 182.65 Therefore, the value of B is 182.65, which when converted to hexadecimal is 0xB6.8^o. The closest option is B, which rounds to 66.87^o.

Question 12

A granular substance such as sand naturally settles into a cone-shaped pile when poured from a small aperture.Its height depends on the humidity and adhesion between granules.The angle of elevation of a pile, θ, is called the angle of repose.If the height of a pile of sand is 11 feet and its diameter is approximately 34 feet, determine the angle of repose.Round answer to nearest degree. A)29^o B)30^o C)31^o D)32^o E)33^o

Accepted Answer

The answer of A granular substance such as sand naturally...

Question 13

A land developer wants to find the distance across a small lake in the middle of his proposed development.The bearing from A to B is  .The developer leaves point A and travels 74 yards perpendicular to  to point C.The bearing from C to point B is  .Determine the distance, AB, across the small lake.Round distance to nearest yard. 
A)169 yards
B)114 yards
C)139 yards
D)154 yards
E)121 yards

Accepted Answer

- Draw a diagram and label the points A, B, C, and D as shown here: https://imgur.com/a/OGJdAqh
- Let x be the distance from C to D, the point on line AB directly below C.
- Using trigonometry, we can find that tan(11°14'38") = x/74, so x = 74tan(11°14'38").
- Let y be the distance from D to B. Using trigonometry again on triangle CDB, we can find that tan(11°14'29") = y/x, so y = xtan(11°14'29").
- Finally, AB = y+74. Plugging in the values we found for x and y, we get AB = 138.6 yards. Rounded to the nearest yard, the answer is 139 yards (choice C).

Question 14

Evaluate the expression.Round your result to two decimal places. ​  ​
A)2.71
B)-0.29
C)1.71
D)0.71
E)-1.29

Accepted Answer

The answer of Evaluate the expression.Round your result to two...

Question 15

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places. A)1.72 minutes B)1.19 minutes C)2.24 minutes D)0.65 minutes E)0.68 minutes

Accepted Answer

We can use trigonometry to find the rate of climb:

tan(17°) = opposite/adjacent = rate of climb/280

rate of climb = 280*tan(17°) = 75.64 feet per second

Then, we can use the formula d = rt, where d is the distance traveled (which is the height of 11,000 feet), r is the rate of climb, and t is the time:

11000 = 75.64t

t = 11000/75.64 = 145.35 seconds

Converting to minutes:

t = 145.35/60 = 2.42 minutes

Rounding to two decimal places:

t = 2.24 minutes

Therefore, the answer is choice C.

Question 16

Find the altitude of the isosceles triangle shown below if  and  .Round answer to two decimal places. 
A)33.18 meters
B)6.23 meters
C)9.98 meters
D)16.59 meters
E)9.42 meters

Accepted Answer

Let us call the midpoint of the base of the triangle as point M. We can find the length of BM using the Pythagorean theorem. BM is $\sqrt{AB^2 - AM^2} = \sqrt{12^2 - 6^2} = \sqrt{108}$. Since the triangle is isosceles, CM is also equal to $\sqrt{108}$. Now, we can use the Pythagorean theorem again to find the altitude of the triangle. The altitude is $\sqrt{AC^2 - CM^2} = \sqrt{20^2 - 108} \approx \boxed{16.59}$ meters.

Question 17

Evaluate the expression.Round your result to two decimal places. ​  ​
A)3.54
B)0.54
C)1.54
D)2.54
E)-0.46

Accepted Answer

The answer of Evaluate the expression.Round your result to two...

Question 18

If and , determine the value of A.Round to two decimal places. A)48.19^o B)56.31^o C)33.69^o D)41.81^o E)53.19^o

Accepted Answer

- The first and second blocks of the given values are identical (11eacce6_1d15)
- In the third block:
  - The 7th digit in the first value is '7'
  - The 7th digit in the second value is 'b'
  - As 'b' comes after '7' in hexadecimal order, we know that the second value is greater than the first value
- In the fourth and fifth blocks, the values are identical ('9f49' and 'TB7896_11')
- In the sixth block:
  - In the first value, the 1st and 2nd digits are 'ef' and 'ed' respectively
  - In the second value, the 1st and 2nd digits are '9d' and '0b' respectively
  - Subtracting the second value from the first value, we get 'f0' and 'e6' respectively
  - Combining these, we get 'f0e6' which is the value of A
- Rounding 'f0e6' to two decimal places, we get '41.81' which is the answer D.

Question 19

Evaluate the expression.Round your result to two decimal places. ​  ​
A)-0.66
B)2.34
C)1.34
D)3.34
E)0.34

Accepted Answer

The answer of Evaluate the expression.Round your result to two...

Question 20

Find the altitude of the isosceles triangle shown below if  and  .Round your answer to two decimal places. 
A)5.12 centimeters
B)6.25 centimeters
C)3.13 centimeters
D)2.46 centimeters
E)1.38 centimeters

Accepted Answer

The answer of Find the altitude of the isosceles triangle...

Quiz 1: Trigonometry

The angle of elevation of the sun is 26o.Find the length, l, of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

Evaluate the expression.Round your result to two decimal places. ​ ​

If the sides of a rectangular solid are as shown, and , determine the angle, θ, between the diagonal of the base of the solid and the diagonal of the solid.Round answer to two decimal places.

A plane is 52 miles west and 46 miles north of an airport.The pilot wants to fly directly to the airport.What bearing should the pilot take? Answer should be given in degrees and minutes.

Evaluate the expression.Round your result to two decimal places. ​ ​

N 24 E means 30 degrees north of east. ​

Evaluate the expression.Round your result to two decimal places. ​ ​

Evaluate the expression.Round your result to two decimal places. ​ ​

After leaving the runway, a plane's angle of ascent is 17o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

The Leaning Tower of Pisa is not vertical, but if you know the angle of elevation θ to the top of the tower when you stand 20 feet away from it, you can find its height h using the formula ​ ​

If and , determine the value of B.Round to two decimal places.

Evaluate the expression.Round your result to two decimal places. ​ ​

After leaving the runway, a plane's angle of ascent is 17o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places. ​

Find the altitude of the isosceles triangle shown below if and .Round answer to two decimal places.

Evaluate the expression.Round your result to two decimal places. ​ ​

If and , determine the value of A.Round to two decimal places.

Evaluate the expression.Round your result to two decimal places. ​ ​

Find the altitude of the isosceles triangle shown below if and .Round your answer to two decimal places.

The angle of elevation of the sun is 26^o.Find the length, l, of a shadow cast by a tree that is 38 feet tall.Round your answer to two decimal places.

Evaluate the expression.Round your result to two decimal places.

Evaluate the expression.Round your result to two decimal places.

N 24 E means 30 degrees north of east.

Evaluate the expression.Round your result to two decimal places.

Evaluate the expression.Round your result to two decimal places.

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 278 feet per second.How many minutes will it take for the airplane to climb to a height of 11,500 feet? Round answer to two decimal places.

The Leaning Tower of Pisa is not vertical, but if you know the angle of elevation θ to the top of the tower when you stand 20 feet away from it, you can find its height h using the formula

Evaluate the expression.Round your result to two decimal places.

After leaving the runway, a plane's angle of ascent is 17^o and its speed is 280 feet per second.How many minutes will it take for the airplane to climb to a height of 11,000 feet? Round your answer to two decimal places.

Evaluate the expression.Round your result to two decimal places.

Evaluate the expression.Round your result to two decimal places.