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 11

A balloon is flying at a height of 80 m. The angle of elevation from a point on the ground to the balloon is 30°. How far is the balloon from the point on the ground (horizontal distance)?

A flagpole is 20 m high. The angle of elevation of its top from a point on the ground is 30°. How far is the point from the base of the flagpole?

A ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m from the wall, what is the angle the ladder makes with the ground?

A man 1.7 m tall observes the top of a building at an angle of elevation of 45°. If he is standing 10 m from the building, what is the height of the building?

A man 1.8 m tall observes the top of a building at an angle of elevation of 30°. If he is standing 20 m from the building, what is the height of the building?

A man observes the top of a tower at an angle of elevation of 30°. He walks 50 m towards the tower and now the angle of elevation is 60°. Find the height of the tower.

A man observes the top of a tower at an angle of elevation of 45°. After walking 30 m towards the tower, the angle of elevation becomes 60°. Find the height of the tower.

A man standing 40 meters away from a building observes the top of the building at an angle of elevation of 30°. Find the height of the building (to the nearest meter).

A man standing on a hill observes a boat at an angle of depression of 20°. If the hill is 100 m high, how far is the boat from the base of the hill?

A man standing on the top of a 50 m high building observes a car on the ground at an angle of depression of 30°. How far is the car from the base of the building?

A person 1.5 m tall observes the top of a tower at an angle of elevation of 60°. If the distance between the person and the tower is 10 m, what is the height of the tower?

A person observes the top of a tower at an angle of elevation of 45°. If the person is standing 50 m from the base, what is the height of the tower?

A tower is 30 m high. From a point on the ground, the angle of elevation to the top of the tower is 45°. How far is the point from the base of the tower?

A tree casts a shadow 12 m long when the angle of elevation of the sun is 45°. What is the height of the tree?

If the angle of depression from the top of a tower to a point on the ground is 45°, and the height of the tower is 20 m, how far is the point from the base of the tower?

If the angle of elevation of the sun is 60°, what is the length of the shadow cast by a pole 5 m high?

If the angle of elevation of the top of a flagpole from a point 24 m away is 45°, what is the height of the flagpole?

The angle of elevation of the top of a tree from a point 15 m away from its base is 60°. What is the height of the tree?

What is the angle of elevation?

A man observes the top of a building at an angle of elevation of 30°. He then walks 80 m towards the building and finds the angle of elevation to be 60°. What is the height of the building?