Question 1

Solve the problem.
-From a boat on the river below a dam, the angle of elevation to the top of the dam is 34°48'. If the top of the dam is 2064 feet above the level of the river, how far is the boat from the base of the dam
(to the nearest foot)?

Accepted Answer

The answer of Solve the problem.
-From a boat on the...

Question 2

From the top of a vertical tower, 310 feet above the the surface of the earth, the angle of depression to a doghouse is 24° 34'. How far is it from the doghouse to the foot of the tower? Round your
Answer to the nearest hundredth.

Accepted Answer

The correct answer is A because the angle of depression is the angle between the horizontal and the line of sight to the doghouse. The tangent of this angle is the ratio of the height of the tower to the distance from the doghouse to the foot of the tower. So, tan(24° 34') = 310/x, where x is the distance from the doghouse to the foot of the tower. Solving for x, we get x = 310/tan(24° 34') = 678.14 ft.

Question 3

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed the angle of depression to the boat is 19° 13'. When the boat stops, the
Angle of depression is 49° 18' . The lighthouse is 200 feet tall. How far did the boat travel from
When it was first noticed until it stopped? Round your answer to the hundredths place.

Accepted Answer

The answer of A person is watching a boat from...

Question 4

A contractor needs to know the height of a building to estimate the cost of a job. From a point 83 feet away from the base of the building, the angle of elevation to the top of the building is found to
Be 44° 10'. Find the height of the building. Round your answer to the hundredths place.

Accepted Answer

The answer of A contractor needs to know the height...

Question 5

Solve the problem.
-From a balloon 1033 feet high, the angle of depression to the ranger headquarters is 53°22'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)?

Accepted Answer

The answer of Solve the problem.
-From a balloon 1033 feet...

Question 6

The angle of elevation from a point on the ground to the top of a tower is 36° 12'. The angle of elevation from a point 164 feet farther back from the tower is 21° 15'. Find the height
Of the tower. Round your answer to the hundredths place.

Accepted Answer

The answer of The angle of elevation from a point...

Question 7

Bob is driving along a straight and level road straight toward a mountain. At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 24° 23'. He then
Drives 1 mile (1 mile = 5280 ft)more and measures the angle of elevation to be 33° 12'. Find the
Height of the mountain to the nearest foot.

Accepted Answer

Using trigonometry, we can solve this problem by setting up equations based on the tangent of the angles given, which is the ratio of the opposite side (height of the mountain, h) to the adjacent side (distance from the mountain). Let x be the distance from the mountain when the first angle was measured. Then, the tangent of the angles gives us two equations:1. tan(24° 23') = h / x2. tan(33° 12') = h / (x - 5280)Solving these equations simultaneously allows us to find the value of h, the height of the mountain. After calculating, the height of the mountain rounds to 7787 feet.

Question 8

In one area, the lowest angle of elevation of the sun in winter is 23° 45'. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high. Round your answer to
The tenths place.

Accepted Answer

The answer of In one area, the lowest angle of...

Question 9

A person is watching a car from the top of a building. The car is traveling on a straight road away from the building. When first noticed the angle of depression to the car is 43° 39' . When the car
Stops, the angle of depression is 21° 53' . The building is 230 feet tall. How far did the car travel
From when it was first noticed until it stopped? Round your answer to the hundredths place.

Accepted Answer

The answer of A person is watching a car from...

Question 10

At an altitude of 2600 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 3 miles away (to the nearest tenth of a degree)? Note that 1 mile = 5280 feet.

Accepted Answer

To find the glide angle, we need to calculate the descent angle using the tangent function, where tangent of the angle = opposite/adjacent. Here, the opposite side is the altitude loss (2600 ft), and the adjacent side is the horizontal distance to the airport (3 miles = 3 * 5280 ft = 15840 ft). Thus, tan(angle) = 2600 / 15840. Using a calculator to find the angle that corresponds to this tangent value gives an angle of approximately 9.3 degrees.

Question 11

When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 36°2'. If Joey is known to be standing 21 feet from the base of the tree, how tall is the tree (to
The nearest foot)?

Accepted Answer

The answer of When sitting atop a tree and looking...

Question 12

A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 42' with the side of the building, how far is the bottom of the ladder from the base of the building?
Round your answer to the hundredths place.

Accepted Answer

To find the distance from the bottom of the ladder to the base of the building, use the sine function: sin(24° 42') = opposite/hypotenuse. The opposite side is the distance from the base of the building, and the hypotenuse is the ladder length (39 ft). Solving for the opposite side gives approximately 16.3 ft.

Question 13

A blimp is 1700 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 83.3° and 25.5°, how far apart are the two stadiums to
The nearest meter?

Accepted Answer

The answer of A blimp is 1700 meters high in...

Question 14

What is the angle of elevation of the sun when a 35-ft flag pole casts a 24-ft shadow? Round to the nearest tenth of a degree.

Accepted Answer

The angle of elevation can be found using the tangent function in trigonometry, where tan(θ) = opposite/adjacent. Here, the opposite side is the height of the flagpole (35 ft) and the adjacent side is the length of the shadow (24 ft). So, tan(θ) = 35/24. Using a calculator to find the angle θ that corresponds to this tangent value gives θ ≈ 55.6°.

Quiz 14: Trigonometry Formerly

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 34°48'. If the top of the dam is 2064 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot) ?

From the top of a vertical tower, 310 feet above the the surface of the earth, the angle of depression to a doghouse is 24° 34'. How far is it from the doghouse to the foot of the tower? Round your Answer to the nearest hundredth.

A contractor needs to know the height of a building to estimate the cost of a job. From a point 83 feet away from the base of the building, the angle of elevation to the top of the building is found to Be 44° 10'. Find the height of the building. Round your answer to the hundredths place.

Solve the problem. -From a balloon 1033 feet high, the angle of depression to the ranger headquarters is 53°22'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot) ?

The angle of elevation from a point on the ground to the top of a tower is 36° 12'. The angle of elevation from a point 164 feet farther back from the tower is 21° 15'. Find the height Of the tower. Round your answer to the hundredths place.

At an altitude of 2600 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 3 miles away (to the nearest tenth of a degree) ? Note that 1 mile = 5280 feet.

When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 36°2'. If Joey is known to be standing 21 feet from the base of the tree, how tall is the tree (to The nearest foot) ?

A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 42' with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place.

A blimp is 1700 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 83.3° and 25.5°, how far apart are the two stadiums to The nearest meter?

What is the angle of elevation of the sun when a 35-ft flag pole casts a 24-ft shadow? Round to the nearest tenth of a degree.

Quiz 14: Trigonometry Formerly

Solve the problem. -From a boat on the river below a dam, the angle of elevation to the top of the dam is 34°48'. If the top of the dam is 2064 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot) ?

From the top of a vertical tower, 310 feet above the the surface of the earth, the angle of depression to a doghouse is 24° 34'. How far is it from the doghouse to the foot of the tower? Round your Answer to the nearest hundredth.

A contractor needs to know the height of a building to estimate the cost of a job. From a point 83 feet away from the base of the building, the angle of elevation to the top of the building is found to Be 44° 10'. Find the height of the building. Round your answer to the hundredths place.

Solve the problem. -From a balloon 1033 feet high, the angle of depression to the ranger headquarters is 53°22'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot) ?

The angle of elevation from a point on the ground to the top of a tower is 36° 12'. The angle of elevation from a point 164 feet farther back from the tower is 21° 15'. Find the height Of the tower. Round your answer to the hundredths place.

In one area, the lowest angle of elevation of the sun in winter is 23° 45'. Find the minimum distance x that a plant needing full sun can be placed from a fence that is 5 feet high. Round your answer to The tenths place.

At an altitude of 2600 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 3 miles away (to the nearest tenth of a degree) ? Note that 1 mile = 5280 feet.

When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 36°2'. If Joey is known to be standing 21 feet from the base of the tree, how tall is the tree (to The nearest foot) ?

A 39-foot ladder is leaning against the side of a building. If the ladder makes an angle of 24° 42' with the side of the building, how far is the bottom of the ladder from the base of the building? Round your answer to the hundredths place.

A blimp is 1700 meters high in the air and measures the angles of depression to two stadiums to the west of the blimp. If those measurements are 83.3° and 25.5°, how far apart are the two stadiums to The nearest meter?

What is the angle of elevation of the sun when a 35-ft flag pole casts a 24-ft shadow? Round to the nearest tenth of a degree.