Worksheet

1

Find the angle of depression from point B to point D, correct to the nearest minute.

2

Find the angle of elevation from point C to point A, rounded to the nearest second.

3

The angle of elevation from an observer to the top of a tree is 35 \degree. The distance between the tree and the observer is d metres and the tree is known to be 1.24 \text{ m} high.

Find the value of d, correct to two decimal places.

4

At a certain time of the day, a light post, 5\text{ m} tall, has a shadow of 9.3 \text{ m}.

Find \theta, the angle of elevation from the end of the shadow to the sun at that time, to the nearest second.

5

Justin is on a ship and observes a lighthouse on a cliff in the distance. The base of the cliff is 934 \text{ m} away from the ship, and the angle of elevation of the top of the lighthouse from Lisa is 19 \degree.

a

If the top of the lighthouse is x \text{ m} above sea level, find the value of x, correct to two decimal places.

b

If the lighthouse is 30 \text{ m} tall, how tall is the cliff? Round your answer to two decimal places.

6

From the top of a cliff, 30 \text{ m} above sea level, two boats are observed to be in the same direction. The angles of depression are 19 \degree and 27 \degree respectively.

a

If the distance between the base of the cliff and the boat furthest away is u \text{ m}, find u to two decimal places.

b

If the distance between the cliff and the closest boat is v \text{ m}, find v to two decimal places.

c

Hence, find the distance between the two boats in metres, correct to one decimal place.

7

A man stands at point A looking at the top of two poles. Pole 1 has a height 12 \text{ m} and an angle of elevation of 25 \degree from point A. Pole 2 has a height 43 \text{ m} and an angle of elevation of 49 \degree from point A.

a

Find the value of x in metres. Round your answer to two decimal places.

b

Find the value of y in metres. Round your answer to two decimal places.

c

Find the distance, d, between the two poles in metres. Round your answer to one decimal place.

8

A fighter jet, flying at an altitude of 2000 \text{ m} is approaching an airport. The pilot measures the angle of depression to the airport to be 13 \degree. One minute later, the pilot measures the angle of depression again and finds it to be 16 \degree.

a

Find the distance AC, to the nearest metre.

b

Find the distance BC, to the nearest metre.

c

Hence, find the distance covered by the jet in that one minute, to the nearest metre.

9

The angle of elevation to the top of a 43-metre high statue is 52 \degree from point A, due west of the statue. The point B is located 35 \text{ m} due south of point A.

a

Find the distance, x, from point A to the base of the statue, correct to two decimal places.

b

Find y, the distance from point B to the base of the statue, correct to one decimal place.

c

Find \theta, the angle of elevation from point B to the top of the statue, correct to the nearest second.

10

From the top of a rocky ledge 274 \text{ m} high, the angle of depression to a boat is 15 \degree. If the boat is d metres from the foot of the cliff, find d, correct to two decimal places.

11

Beth measures the angle of elevation to the top of a tree, from a point 22 \text{ m} away from the base, to be 42\degree. Find the height of the tree to the nearest metre.

12

Dave is standing 280 \text{ m} from a building and measures the angle of elevation of the top of the building to be 17 \degree.

a

Find the difference in height between the top of the building and Dave's eye, correct to two decimal places.

b

If Dave's eye is 170\text{ cm} from the ground, what is the height of the building? Round your answer to one decimal place.

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applies trigonometry to solve problems, including problems involving bearings