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Heights and Distances

Math ⇒ Trigonometry

Heights and Distances starts at 10 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Heights and Distances. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.
See sample questions for grade 12
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 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 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 vertical pole 10 m high casts a shadow 10 m long. What is the angle of elevation of the sun?
A vertical pole and a vertical tower are on the same level ground. The angle of elevation of the top of the pole from the foot of the tower is 60°, and the angle of elevation of the top of the tower from the foot of the pole is 30°. If the pole is 20 m high, find the height of the tower.
If the angle of depression from the top of a lighthouse 60 m high to a boat is 45°, how far is the boat from the base of the lighthouse?
If the angle of elevation of the sun is 45°, what is the length of the shadow cast by a pole of height 10 m?
If the angle of elevation of the top of a tower from a point on the ground is increased from 30° to 60% as the observer moves 40 m closer to the tower, find the height of the tower.
The angle of elevation of the top of a building from a point 40 m away from its foot is 45°. What is the height of the building?
The angle of elevation of the top of a building from a point on the ground is 45°. If the point is 30 m away from the building, what is the height of the building?
The angle of elevation of the top of a tower from a point 50 m away from its foot is 37°. Find the height of the tower. (tan 37° = 0.7536)