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6.04 Angles of elevation and depression

Worksheet
Angles of elevation and depression
1

A man standing at the top of the tower at point B, is looking at the ground at point C. Identify the angle of depression in the following figure:

2

Find the angle of depression from point B to point C in the diagram shown. Round your answer to two decimal places.

3

Find x, the angle of elevation to point A from point C. Round your answer to two decimal places.

4

The person in the picture sights a pigeon above him. Find the angle of elevation, \theta, to two decimal places.

5

Sally measures the angle of elevation to the top of a tree from a point 20 \text{ m} away to be 43 \degree. Find the height of the tree, h, to the nearest whole number.

6

A boy flying his kite releases the entire length of his string which measures 27\text{ m}, so that the kite is 18\text{ m} above him.

If the angle the string makes with the horizontal ground is \theta, find \theta to two decimal places.

7

A helicopter is 344\text{ m} away from its landing pad. If the angle of depression to the landing pad is 32 \degree, find x, the height of the helicopter above the ground, to the nearest metre.

8

The final approach of an aeroplane when landing requires the pilot to adjust the angle of descent to about 3 \degree as shown in the diagram below. If the plane is 12 \text{ m} above the runway and has d \text{ m} until touchdown, find d to the nearest metre.

9

The airtraffic controller is communicating with a plane in flight approaching an airport for landing. The plane is 10\,369 \text{ m} above the ground and is still 23\,444 \text{ m} from the runway.

If \theta \degree is the angle at which the plane should approach, find \theta to one decimal place.

Applications
10

Fred is on a ship and observes a lighthouse on a cliff in the distance. The base of the cliff is 651 \,\text{m} away from the ship, and the angle of elevation of the top of the lighthouse from Fred is 35 \degree.

a

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

b

If the lighthouse is 30 metres tall, how tall is the cliff that the lighthouse stands on? Round your answer correct to two decimal places.

11

Buzz is standing 250 \,\text{m} from a building and measures the angle of elevation of the top of the building to be 27 \degree.

a

If the difference in height between the top of the building and Buzz's eye is h \,\text{m}, find h correct to two decimal places.

b

If Buzz's eye is 172 \,\text{cm} from the ground, find the height of the building correct to one decimal place.

12

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

13

Amelia measures the angle of elevation to the top of a tree from a point, 29 \text{ m} away from the base, to be 31 \degree. Find the height of the tree, h, to the nearest metre.

14

The angle of elevation from an observer to the top of a tree is 18 \degree. If the distance between the tree and the observer is d \text{ m} and the tree is known to be 3.53 \text{ m} high, find the value of d to two decimal places.

15

At a certain time of the day a light post, 6 \text{ m} tall, has a shadow of 5.8 \text{ m}. If the angle of elevation of the sun at that time is \theta \degree, find \theta to two decimal places.

16

A man stands at point A looking at the top of two poles. Pole 1 has a height 8 \text{ m} and an angle of elevation of 34 \degree from point A. Pole 2 has a height 25 \text{ m} and an angle of elevation of 57 \degree from point A.

a

Find the distance from A to B, to two decimal places.

b

Find the distance from A to C, to two decimal places.

c

Hence, find BC, the distance between the two poles in metres. Round your answer to one decimal place.

17

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.

18

A ramp of length 311\text{ cm} needs to ascend at an angle between 10 \degree and 20 \degree for it to be safe to use.

a

If the height of the ramp is 152\text{ cm}, and the angle the ramp makes with the ground is x, find x to two decimal places.

b

If the height of the ramp is 25\text{ cm} , and the angle the ramp makes with the ground is y, find y to two decimal places.

c

If the height of the ramp is 100\text{ cm}, and the angle the ramp makes with the ground is z, find z to two decimal places.

d

Hence, at which height is the ramp safe?

19

From a point 15\text{ m} due north of a tower, the angle of elevation of the tower is 32 \degree.

a

Find the height of the tower h. Round your answer to two decimals places.

b

Find the size \theta of the angle of elevation of the tower at a point 20\text{ m} due east of the tower. Round your answer to the nearest degree.

20

Two hot air balloons are tied to the ground below, each at a different location. An observer at each location measures the angle of elevation to the opposite balloon. The observers are 1600 \text{ m} apart as shown in the diagram:

a

Calculate the difference in height between the two balloons. Round your answer to the nearest metre.

b

Hence, find the direct distance between the two balloons. Round your answer to the nearest metre.

21

Roald is standing at point P and observes two poles, AB and CD, of different heights. P, \, B, and D are on horizontal ground:

From P, the angles of elevation to the top of the poles at A and C are 29 \degree and 18 \degree respectively. Roald is 16 \text{ m} from the base of pole AB. The height of pole CD is 7 \text{ m}.

a

Calculate the distance from Roald to the top of pole CD, to two decimal places.

b

Calculate the distance from Roald to the top of pole AB, to two decimal places.

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Solve right-angled triangle problems including those involving direction and angles of elevation and depression.

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