Free Test Heights and Distances – JEE

Q1: The angle of elevation of the top of a tower from a point on the ground is 30°. If the height of the tower is 50 m, find the distance of the point from the base of the tower.

A. 86.6 m B. 100 m C. 50√3 m D. 25 m

Q2: A man observes the top of a building at an angle of elevation of 45°. If the building is 40 m high, find the distance of the man from the building.

A. 40 m B. 20√2 m C. 60 m D. 40√2 m

Q3: If the angle of depression from the top of a lighthouse to a boat is 60° and the height of the lighthouse is 100 m, how far is the boat from the base?

A. 57.7 m B. 86.6 m C. 50 m D. 173.2 m

Q4: Two towers of heights 30 m and 50 m stand apart. The angle of elevation of the top of the taller tower from the base of the shorter one is 60°. Find the distance between the towers.

A. 20 m B. 40 m C. 34.6 m D. 45.3 m

Q5: The angle of elevation to the top of a pole is 60° from a point 10 m away. Find the height of the pole.

A. 5√3 m B. 10√3 m C. 10 m D. 15 m

Q6: From a point 50 m from the base, the top of a tower is observed at an angle of 45°. Height of the tower is:

A. 25 m B. 50√2 m C. 50 m D. 100 m

Q7: If the shadow of a 20 m pole is 20√3 m long, what is the angle of elevation of the sun?

A. 30° B. 45° C. 60° D. 15°

Q8: The top of a tower makes an angle of elevation of 60° at a point A. If height of tower is 30√3 m, distance from point A is:

A. 30 m B. 60 m C. 90 m D. 15 m

Q9: A man observes a balloon at an elevation of 30°. If the balloon is 100 m high, how far is the man from it (horizontally)?

A. 173.2 m B. 50 m C. 86.6 m D. 100 m

Q10: From a point 20 m from a tower, the angle of elevation of the top is 45°. Height of tower is:

A. 10 m B. 20√2 m C. 20 m D. 40 m

Q11: Two persons standing on opposite sides of a tower measure angle of elevation to be 30° and 60°. If distance between them is 40 m, height of tower is:

A. 10 m B. 20 m C. 17.3 m D. 30 m

Q12: A pole 20 m high casts a shadow of 20 m. What is the angle of elevation of the sun?

A. 30° B. 60° C. 45° D. 90°

Q13: If the angle of depression to a car from a cliff 50 m high is 30°, how far is the car from the base?

A. 86.6 m B. 100 m C. 50√3 m D. 25 m

Q14: A tower subtends an angle of 60° at a point A and 30° at another point B in line with A. If AB = 100 m, find height of the tower.

A. 50 m B. 57.7 m C. 86.6 m D. 40 m

Q15: The angle of elevation of the top of a lighthouse is 45° from a boat. If the lighthouse is 80 m high, the distance of the boat is:

A. 80 m B. 160 m C. 40 m D. 100 m

Q16: A balloon rises vertically at 10 m/s. After 10 seconds, the angle of elevation is 30°. Find distance from observer.

A. 100 m B. 173.2 m C. 86.6 m D. 200 m

Q17: An observer notes that the angle of elevation of a tower increases from 30° to 60° as he walks 100 m closer. Find height.

A. 50 m B. 100 m C. 86.6 m D. 57.7 m

Q18: The height of a tower is 60 m. What is the length of the shadow if angle of elevation is 60°?

A. 30 m B. 34.6 m C. 60√3 m D. 60/√3 m

Q19: A man observes top of a tree at angle of elevation 60°. Tree height is 20√3 m. Find distance from tree.

A. 10 m B. 20 m C. 30 m D. 40 m

Q20: A building is observed at angle of elevation 45° from a point. If observer is 10 m tall and total height is 60 m, distance is:

A. 50 m B. 70 m C. 100 m D. 20 m

Quiz for Heights and Distances