Heights and Distances

high importance~2 Q in Tier 117 formulas⚡ 10 shortcuts5 subtopics

Overview Learn (5)Formulas (17)Examples (5)Practice (67)

Exam-level questions worked step by step. Try each one yourself first — then expand the solution and compare routes.

Q1.

The angle of elevation of the top of a 50 m high tower from a point on the ground is $45^\circ$ . Find the distance of the point from the base of the tower.

Q2.

The shadow of a tower is $40\sqrt{3}$ m long when the sun's elevation is $30^\circ$ . Find the height of the tower.

Q3.

From the top of a 100 m high cliff, the angle of depression of a ship is $30^\circ$ . Find the distance of the ship from the base of the cliff.

Q4.

Walking 40 m towards a tower, the angle of elevation of its top changes from $30^\circ$ to $60^\circ$ . Find the height of the tower.

Q5.

A statue stands on a 30 m high pedestal. From a point on the ground, the angle of elevation of the top of the pedestal is $45^\circ$ and that of the top of the statue is $60^\circ$ . Find the height of the statue.

Ready? Take the 67-question test →