Heights and Distances
Math ⇒ Trigonometry
Heights and Distances starts at 10 and continues till grade 12.
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See sample questions for grade 12
A balloon is observed at an angle of elevation of 60° from a point 100 m from the point on the ground directly below the balloon. Find the height of the balloon above the ground.
A ladder 20 m long is placed against a wall such that it makes an angle of 60° with the ground. How high does the ladder reach on the wall?
A man 1.7 m tall observes the top of a building at an angle of elevation of 30°. If he is standing 40 m from the building, find the height of the building.
A man 1.8 m tall observes the top of a building at an angle of elevation of 45°. If he is standing 20 m from the building, find the height of the building.
A man observes the top of a tower at an angle of elevation of 30°. He then walks 50 m towards the tower and finds the angle of elevation to be 60°. Find the height of the tower.
A man observes the top of a tower at an angle of elevation of 45°. He walks 30 m towards the tower and the angle of elevation becomes 60°. Find the height of the tower.
A man observes the top of a tree at an angle of elevation of 60°. If the man is standing 10 m from the base of the tree, find the height of the tree.
A man standing at a distance of 80 m from a tower finds the angle of elevation of the top of the tower to be 30°. What is the height of the tower?
A man standing on a hill observes the angle of depression of a boat as 45°. If the hill is 80 m high, how far is the boat from the base of the hill?
A man standing on the deck of a ship, 10 m above water level, observes the angle of elevation of the top of a cliff as 60° and the angle of depression of the base as 30°. Find the height of the cliff.
A man standing on the ground finds the angle of elevation of the top of a tree to be 30°. If the tree is 15 m high, how far is the man from the foot of the tree?
A man standing on the ground observes the top of a tower at an angle of elevation of 30°. If the height of the tower is 50 m, find the distance of the man from the foot of the tower. (Give your answer correct to two decimal places.)
A tower and a flagstaff stand on the same base. The angle of elevation of the top of the flagstaff is 60° and that of the top of the tower is 45°. If the tower is 20 m high, find the height of the flagstaff.
A tower is 60 m high. At a certain distance from the tower, the angle of elevation of its top is 45°. Find the distance of the point from the foot of the tower.
A balloon is observed at an angle of elevation of 60° from a point 100 m from the point on the ground directly below the balloon. Find the height of the balloon above the ground.
A ladder 20 m long is placed against a wall such that it makes an angle of 60° with the ground. How high does the ladder reach on the wall?
A man 1.7 m tall observes the top of a building at an angle of elevation of 30°. If he is standing 40 m from the building, find the height of the building.
A man 1.8 m tall observes the top of a building at an angle of elevation of 45°. If he is standing 20 m from the building, find the height of the building.
Which trigonometric ratio is used to relate the height of an object and the distance from the observer to the object in problems involving angles of elevation? (1) Sine (2) Cosine (3) Tangent (4) Secant
True or False: The angle of depression is always measured from the horizontal downward.
