What is the line drawn from the observer’s eye to the object being viewed called?
(A) Line of sight
(B) Height line
(C) Base line
(D) Angle line
Answer: (A)

What is the angle called when an observer raises their head to look at an object?
(A) Angle of depression
(B) Angle of elevation
(C) Right angle
(D) Radius angle
Answer: (B)

What is the angle called when an observer lowers their head to look at an object?
(A) Angle of depression
(B) Angle of elevation
(C) Zero angle
(D) Inclination angle
Answer: (A)

If the angle of elevation of the top of a tower is 45° and the observer is 20 m away from its base, what is the height of the tower?
(A) 10 m
(B) 20 m
(C) 30 m
(D) 40 m
Answer: (B)

The height of a pole is 10 m. If the shadow of the pole is 10 m, what is the angle of elevation of the sun?
(A) 30°
(B) 45°
(C) 60°
(D) 90°
Answer: (B)

A ladder is leaning against a wall, forming a 60° angle with the ground. If the foot of the ladder is 5 m away from the wall, what is the height of the ladder’s top?
(A) 5 m
(B) 5√3 m
(C) 10 m
(D) 10√3 m
Answer: (B)

A 1.5 m tall observer is standing 28.5 m away from a chimney. The angle of elevation from their eyes to the top of the chimney is 45°. What is the height of the chimney?
(A) 25 m
(B) 28.5 m
(C) 30 m
(D) 35 m
Answer: (C)

A kite is flying at a height of 50 m with a string inclined at 30° to the ground. What is the length of the string if there is no slack?
(A) 50 m
(B) 50√3 m
(C) 100 m
(D) 100√3 m
Answer: (C)

If a person looks at a tree 40 m away with an angle of elevation of 60°, what is the approximate height of the tree?
(A) 40√3 m
(B) 20 m
(C) 20√3 m
(D) 10 m
Answer: (A)

What trigonometric ratio is used to find the height of an object when the base and angle of elevation are known?
(A) Sine
(B) Cosine
(C) Tangent
(D) Cosecant
Answer: (C)

The angle of elevation of the top of a lighthouse from a ship is 30°. If the height of the lighthouse is 100 m, what is the horizontal distance of the ship from the lighthouse?
(A) 50√3 m
(B) 100√3 m
(C) 150 m
(D) 200 m
Answer: (B)

A flagpole is mounted on top of a building. If the angle of elevation to the top of the flagpole is 60° and to the top of the building is 45°, what is the height of the flagpole if the building is 20 m high?
(A) 10 m
(B) 12 m
(C) 15 m
(D) 20 m
Answer: (C)

A man on a boat observes the top of a lighthouse at an angle of elevation of 60°. If the height of the lighthouse is 75 m, how far is the boat from the base of the lighthouse?
(A) 50 m
(B) 75√3 m
(C) 100 m
(D) 125 m
Answer: (B)

If an observer moves 20 m closer to a building, the angle of elevation to its top increases from 30° to 60°. What is the height of the building?
(A) 20 m
(B) 30 m
(C) 40 m
(D) 50 m
Answer: (C)

If the angle of elevation of the sun is 45°, what is the relationship between the height of an object and its shadow?
(A) Shadow is twice the height
(B) Height and shadow are equal
(C) Shadow is half the height
(D) There is no relation
Answer: (B)

If the angles of elevation to the top and bottom of a tower from a building’s roof are 30° and 45°, and the building is 20 m high, what is the height of the tower?
(A) 20√3 m
(B) 30 m
(C) 40 m
(D) 50 m
Answer: (A)

A helicopter is hovering at a height of 500 m above the ground. If the angle of depression to a point on the ground is 60°, what is the horizontal distance of the point from the helicopter?
(A) 250√3 m
(B) 500√3 m
(C) 750 m
(D) 1000 m
Answer: (B)

The angles of depression of two points on the ground from a balloon are 45° and 60°. If the two points are 50 m apart, what is the height of the balloon?
(A) 50 m
(B) 50√3 m
(C) 75 m
(D) 100 m
Answer: (B)

A building casts a shadow of 30 m when the angle of elevation of the sun is 45°. What is the height of the building?
(A) 15 m
(B) 30 m
(C) 45 m
(D) 60 m
Answer: (B)

A tower’s shadow is 40 m longer when the sun’s altitude is 30° compared to when it is 60°. What is the height of the tower?
(A) 10√3 m
(B) 20√3 m
(C) 30√3 m
(D) 40√3 m
Answer: (B)

A 50 m tall building has a flagpole on top. The angle of elevation of the flagpole’s top from a point 30 m away is 60°, and to the top of the building is 45°. What is the height of the flagpole?
(A) 10 m
(B) 20 m
(C) 30 m
(D) 40 m
Answer: (B)

The top of a 40 m tall tower is observed from a certain point with an angle of elevation of 30°. What is the distance of the observer from the base of the tower?
(A) 40√3 m
(B) 40/√3 m
(C) 40 m
(D) 20√3 m
Answer: (B)

From the top of a 100 m high lighthouse, the angles of depression of two boats are 30° and 45°. What is the distance between the two boats?
(A) 73.2 m
(B) 100 m
(C) 115.5 m
(D) 200 m
Answer: (C)

A tree breaks due to a storm, and the top touches the ground making a 30° angle with it. If the broken part is 8 m long, what was the original height of the tree?
(A) 12 m
(B) 14 m
(C) 16 m
(D) 20 m
Answer: (C)

The angle of elevation of the top of a tower from a point on the ground is 45°. If the height of the tower is doubled, what will be the new angle of elevation from the same point?
(A) 60°
(B) 75°
(C) 90°
(D) 30°
Answer: (A)

A helicopter is hovering at a height of 800 m. If the angle of depression to a car on the ground is 45°, what is the horizontal distance between the helicopter and the car?
(A) 400 m
(B) 800 m
(C) 800√2 m
(D) 1600 m
Answer: (B)

A building and a tree are 50 m apart. The angles of elevation of the top of the tree from the building and the top of the building from the tree are 30° and 45°, respectively. What is the height of the tree?
(A) 50 m
(B) 70 m
(C) 90 m
(D) 100 m
Answer: (C)

A person observes the top of a tower at an angle of elevation of 30°. If they move 50 m closer, the angle becomes 60°. What is the height of the tower?
(A) 50 m
(B) 60 m
(C) 75 m
(D) 100 m
Answer: (B)

The angles of depression of two ships from the top of a lighthouse are 30° and 60°. If the lighthouse is 120 m high, what is the distance between the two ships?
(A) 120 m
(B) 138.6 m
(C) 200 m
(D) 240 m
Answer: (D)

A 30 m tall building casts a shadow of 30√3 m. What is the angle of elevation of the sun?
(A) 30°
(B) 45°
(C) 60°
(D) 90°
Answer: (A)

A balloon is tied with a 100 m long rope and is flying at a 60° angle with the ground. What is the height of the balloon?
(A) 50 m
(B) 86.6 m
(C) 100 m
(D) 120 m
Answer: (B)

A tower’s shadow is 100 m longer when the sun’s angle is 30° compared to when it is 60°. What is the height of the tower?
(A) 50 m
(B) 75 m
(C) 100 m
(D) 125 m
Answer: (C)

A bridge is 20 m above a river. The angles of depression of two boats are 45° and 60°. What is the distance between the boats?
(A) 10√3 m
(B) 20 m
(C) 20√3 m
(D) 40 m
Answer: (C)

A flagpole is mounted on a building. If the angles of elevation to the top of the flagpole and the building are 60° and 45°, and the height of the building is 10 m, what is the height of the flagpole?
(A) 5 m
(B) 10 m
(C) 12.32 m
(D) 15 m
Answer: (C)

From the top of a 75 m high building, a person sees a car approaching with an angle of depression changing from 30° to 60° in 6 seconds. What is the car’s speed?
(A) 10 m/s
(B) 15 m/s
(C) 20 m/s
(D) 25 m/s
Answer: (B)

The height of a building is twice the length of its shadow. What is the angle of elevation of the sun?
(A) 30°
(B) 45°
(C) 60°
(D) 75°
Answer: (C)

A hill is observed at an angle of elevation of 15°. After moving 1 km towards it, the angle becomes 30°. What is the height of the hill?
(A) 0.5 km
(B) 1 km
(C) 1.5 km
(D) 2 km
Answer: (A)

A tower and a tree are 80 m apart. If their angles of elevation from a common point are 45° and 60°, what is the height difference between them?
(A) 40 m
(B) 50 m
(C) 60 m
(D) 80 m
Answer: (A)

A ladder leans against a wall, forming a 75° angle with the ground. If the ladder is 20 m long, how far is the base from the wall?
(A) 5.18 m
(B) 6.45 m
(C) 7.42 m
(D) 8.91 m
Answer: (C)

A tower’s height is three times the length of its shadow. What is the angle of elevation of the sun?
(A) 30°
(B) 45°
(C) 60°
(D) 75°
Answer: (D)

The angle of elevation of a tower from a point 50 m away is 30°. What is the height of the tower?
(A) 25 m
(B) 50 m
(C) 50√3 m
(D) 25√3 m
Answer: (D)

A 1.5 m tall person is standing 40 m away from a lamp post. The angle of elevation of the top of the post is 30°. What is the height of the lamp post?
(A) 10 m
(B) 15 m
(C) 20 m
(D) 25 m
Answer: (C)

A kite is flying at a height of 75 m. If the string makes a 60° angle with the ground, what is the length of the string (assuming no slack)?
(A) 100 m
(B) 125 m
(C) 150 m
(D) 175 m
Answer: (C)

A tower is 30 m high. From a point on the ground, the angle of elevation of its top is 45°. What is the distance of the observer from the tower?
(A) 30√2 m
(B) 30 m
(C) 15√2 m
(D) 60 m
Answer: (B)

From a ship in the sea, the angle of elevation to the top of a 200 m cliff is 45°. How far is the ship from the base of the cliff?
(A) 100 m
(B) 150 m
(C) 200 m
(D) 250 m
Answer: (C)

If a tree casts a 20 m shadow when the sun’s altitude is 60°, what is the height of the tree?
(A) 10√3 m
(B) 20√3 m
(C) 30√3 m
(D) 40√3 m
Answer: (B)

A ladder leans against a wall, forming a 45° angle with the ground. If the ladder is 10 m long, how high does it reach on the wall?
(A) 5√2 m
(B) 10 m
(C) 5 m
(D) 10√2 m
Answer: (A)

A vertical pole of 12 m has a shadow of 12 m. What is the angle of elevation of the sun?
(A) 30°
(B) 45°
(C) 60°
(D) 75°
Answer: (B)

The angles of elevation of the top of a tower from two points on the ground, 100 m apart, are 30° and 45°. What is the height of the tower?
(A) 50 m
(B) 75 m
(C) 100 m
(D) 125 m
Answer: (B)

A flagpole casts a 25 m shadow when the sun’s angle is 30°. What is the height of the flagpole?
(A) 25√3 m
(B) 50 m
(C) 75 m
(D) 100 m
Answer: (A)