1Choose the correct answer. What is the angle between the line of sight and the horizontal line called when we look at an object below us? (angle of depression, acute angle, angle of elevation, right angle)
2Choose the correct answer. What is the angle between the line of sight and the horizontal line called when we look at an object above us? (angle of depression, acute angle, angle of elevation, right angle)
3Choose the correct answer. If the angle of elevation of an object seen from a place is 0°, where is the object? (above, below, at the level of the eye, cannot be seen)
4Choose the correct answer. When the angle of elevation of the top of a pole from a place is 45°, how is the height of the pole related to its distance from that place? (height > distance, height < distance, equal, no relation)
5Choose the correct answer. As the angle of elevation of the top of a tower seen from a place increases, what happens to the distance of that place from the tower? (increases, decreases, stays the same, no relation)
6Choose the correct answer. What angle of elevation is formed when the top of a tree \( 10\sqrt{3} \) m tall is observed from a point 10 m away from it? (30°, 45°, 60°, 120°)
7In right-angled triangle ABC, the right angle is at B, AB = 20 m and ∠C = 45°. Find y = AC.
8In right-angled triangle PQR, the right angle is at Q, ∠R = 30° and QR = 10 m. Find x = PQ.
9AB = x is vertical with the right angle at B. D and C are on the ground on the same side, with DB = 30 m and CB = 10 m. ∠ADB = 30° and ∠ACB = θ. Find x and θ.
10LB = x is vertical with the right angle at B. N and P lie on the ground on the same side, NP = 45 m and PB = y. ∠LNB = 30° and ∠LPB = 45°. Find x and y.
11AB = 50 m is a building, AE is the horizontal line at its top and CD is a post, with DF parallel to CB and F on AB. The angle of depression of D from A is 30° and that of C is 45°. Find x = CD and y = CB.
12WT = 40 m is vertical with T on the ground between U and V. UT = y, TV = x, ∠WUT = 30° and ∠WVT = 45°. Find x and y.
13A point on the roof of a house is seen from a point on the ground at an angle of elevation of 60°. After moving 50 m farther away, the angle of elevation is 30°. Find the height of the house.
14From two points on level ground on the same side of a 30 ft pole, the angles of elevation of its top are 60° and 45°. Find the distance between the two points.
15From the top of a hill 500 m high, two points on the ground on the same side are seen at angles of depression of 60° and 30°. Find the distance between the points.
16From the roof of a house, two people sitting 10 ft apart in a straight line on one side of the yard are seen at angles of depression of 60° and 45°. Find the height of the house.
17From two points 40 m and 36 m from the foot of a pole, on the same side, the angles of elevation of its top are complementary. Find the height of the pole.
18Two poles are 50 m apart and one is twice as tall as the other. From the point midway between them, the angles of elevation of their tops are complementary. Find the heights of the poles.
19The shadow of a pole on level ground is 50 m longer when the sun's altitude is 30° than when it is 60°. Find the height of the pole.
20The shadow of a 35 ft pole on level ground is x ft longer when the sun's altitude is 30° than when it is 45°. Find x.
21From the roof of a building 30 m high, the angles of depression of the top and the foot of a column are 45° and 60°. Find the height of the column.
22The pinnacle of a temple is seen from the roof and from the foot of a building 20 m high. The angle of depression from the roof is 60° and the angle of elevation from the foot is 30°. Find the height of the temple.
23A national flag stands on top of a tower. From a point 100 m from the foot of the tower, the angles of elevation of the top of the tower and the top of the flag are 45° and 60°. Find the height of the flag.
24A man 1.8 m tall sees the roof of a house and the top of a window at angles of elevation of 45° and 30°. The top of the window is 20 m above the ground. Find the height of the house.
25From the foot and the roof of a house 15 m high, the angles of elevation of the top of a column are 60° and 45°. Find the height of the column.
26An aeroplane flying level at a height of 6000 m is seen from a point on the ground at an angle of elevation of 30°. After 10 seconds it is seen from the same point at 45°. Find its speed in km per hour.
27Two poles of equal height stand on opposite sides of a road 30 m wide. From a point on the road between them, the angles of elevation of their tops are 60° and 30°. Find the height of the poles and the distances of the point from them.
28A man 1.6 m tall stands midway between two poles and sees their tops at angles of elevation of 60° and 45°. The shorter pole is 41.6 m high. Find the height of the taller pole and the distance between the poles.
29A point divides a pole in the ratio 4:5 from the ground. Both parts subtend equal angles at a point on the ground 20 m from the foot. Find the height of the pole.
30A flag 5 m long stands on a tower. From a point on the ground, the tower and the flag subtend angles of 45° and 15°. Find the height of the tower.
31Two poles of equal height stand apart. A man standing between them sees each top at an angle of elevation of 45°. He walks 20 m towards one pole and sees its top at 60°. (a) Draw the diagram. (b) Find the height of the poles. (c) Find the distance between them. (d) Why does the angle of elevation increase as he walks closer?
32A 10 m ladder is placed against the outer wall of a building, touching it at a point 4 m below the roof. The angle of elevation of the roof from the foot of the ladder is 60°. (a) Draw the diagram. (b) At what height does the ladder touch the wall? (c) How far is its foot from the building? (d) Find the angle of elevation, from the foot of the ladder, of the point 20 m below the roof.
33Explain why the angle of depression of a boat seen from the top of a lighthouse equals the angle of elevation of the top of the lighthouse seen from the boat.
34A kite is flying on a straight string 60 m long, making an angle of 30° with the level ground. How high is the kite?
35At a certain time the shadow of a pole is exactly as long as the pole. What is the altitude of the sun?