Some Applications of Trigonometry Practice Questions

Class 10 · Mathematics · 1290 free MCQs with instant results and detailed explanations.

1290

Total

431

Easy

605

Medium

254

Hard

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Topics in Some Applications of Trigonometry

Angle of Depression 468

Heights and Distances 389

Angle of Elevation 433

Sample Questions from Some Applications of Trigonometry

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Easy

From the top of a 15-meter high building, the angle of depression to a point on the ground is 30 degrees. How far is the point from the base of the building?

A. 15√3 meters

B. 15 meters

C. 30 meters

D. 10 meters

Show Answer & Explanation

Correct Answer: A

Using tan(30°) = height/distance, we find the distance as 15√3 meters.

Easy

A person is standing 10 meters away from a pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?

A. 10√3 meters

B. 5 meters

C. 10 meters

D. 15 meters

Show Answer & Explanation

Correct Answer: A

Using tan(60°) = height/10, we find the height of the pole as 10√3 meters.

Easy

If the angle of elevation of a flagpole from a point on the ground is 45 degrees and the distance from the point to the base of the flagpole is 10 meters, what is the height of the flagpole?

A. 5 m

B. 10 m

C. 15 m

D. 20 m

Show Answer & Explanation

Correct Answer: B

At 45 degrees, the height and distance are equal. Thus, height = distance = 10 m.

Medium

If the angle of elevation to the top of a hill from a point 100 m away is 45 degrees, what is the height of the hill?

A. 50 m

B. 100 m

C. 70.7 m

D. 30 m

Show Answer & Explanation

Correct Answer: B

At 45 degrees, height = distance × tan(45) = 100 × 1 = 100 m.

Medium

What is the height of a building if a person standing 60 m away measures the angle of elevation to the top of the building as 45 degrees?

A. 30 m

B. 45 m

C. 60 m

D. 75 m

Show Answer & Explanation

Correct Answer: C

For an angle of 45 degrees, height = distance × tan(45 degrees) = 60 × 1 = 60 m.

Medium

A person is standing 30 m away from a tree. If the angle of elevation to the top of the tree is 45 degrees, how tall is the tree?

A. 30 m

B. 15 m

C. 45 m

D. 60 m

Show Answer & Explanation

Correct Answer: A

At an angle of 45 degrees, the height of the tree is equal to the distance from the tree. Therefore, the height is 30 m.

Medium

An observer is 20 m away from the foot of a tree, and the angle of elevation to the top of the tree is 60 degrees. How tall is the tree?

A. 20√3 m

B. 10 m

C. 20 m

D. 30 m

Show Answer & Explanation

Correct Answer: A

Applying the tangent function, height = distance * tan(60°) = 20 * √3 = 20√3 m.

Hard

From a point 100 m away from the base of a building, the angle of elevation to the top of the building is 60 degrees. How tall is the building?

A. 100 m

B. 50 m

C. 86.6 m

D. 173.2 m

Show Answer & Explanation

Correct Answer: C

Using the formula h = d * tan(θ), where d is the distance from the base and θ is the angle of elevation, we find the height.

Hard

If a kite is flying at a height of 30 m above the ground and it is 40 m away horizontally from the observer, what is the angle of elevation of the kite?

A. 36.87 degrees

B. 45 degrees

C. 53.13 degrees

D. 60 degrees

Show Answer & Explanation

Correct Answer: A

The angle of elevation can be determined using the formula θ = tan^(-1)(height/distance) = tan^(-1)(30/40).

Q10

Hard

A building is 80 m tall. From the top of the building, the angle of depression to the ground is 45 degrees. How far is the person on the ground from the base of the building?

A. 80 m

B. 40 m

C. 60 m

D. 100 m

Show Answer & Explanation

Correct Answer: A

In this scenario, the angle of depression of 45 degrees implies that the height equals the distance from the base due to the properties of right triangles.

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Some Applications of Trigonometry — Class 10 Mathematics Practice Questions Online

This page contains 1290 practice MCQs for the chapter Some Applications of Trigonometry in Class 10 Mathematics. The questions are organized by difficulty — 431 easy, 605 medium, 254 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.