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Class 10 Maths

Trigonometry and Triangles Maths Class 10

NCERT Class 10 Mathematics – Trigonometry and Triangles Quiz

NCERT Class 10 Mathematics – Trigonometry and Triangles Quiz

Multiple Choice Questions

1. In a right-angled triangle ABC, right-angled at B, if tan A = 1/√3, what is the value of sin A?

a) 1/3
b) 1/2
c) √3/2
d) √2/2

2. The angle of elevation of the top of a tower from a point on the ground is 30°. If the height of the tower is 50 meters, how far is the point from the base of the tower?

a) 25√3 meters
b) 50√3 meters
c) 75√3 meters
d) 100√3 meters

3. If sin A = 3/5, determine the value of cos A.

a) 3/5
b) 4/5
c) 5/3
d) 5/4

4. Find the value of tan 45° + cot 45°.

a) 1
b) √2
c) 2
d) 3

5. In triangle ABC, if angle A = 60° and angle B = 30°, what is angle C?

a) 60°
b) 75°
c) 90°
d) 120°

6. What is the value of sin²θ + cos²θ?

a) 0
b) 1
c) 2
d) Depends on θ

7. If cos A = 5/13, what is the value of sin A?

a) 5/13
b) 12/13
c) 13/5
d) 13/12

8. What is the value of sec²θ – tan²θ?

a) 0
b) 1
c) 2
d) Depends on θ

9. In a right-angled triangle, if one acute angle is 30°, what is the other acute angle?

a) 30°
b) 45°
c) 60°
d) 90°

10. What is the value of cosec 90°?

a) 0
b) 1
c) Undefined
d) ∞

Fill in the Blanks

1. The height of a building is 40 meters, and the angle of elevation from a point 30 meters away from its base is θ. The value of tan θ is _______.

2. If cos B = 0.6, the value of sin B is _______.

3. The value of sin 30° + cos 60° is _______.

4. In triangle ABC, if angle C = 90° and AB = 10, the length of AC if angle A = 30° is _______.

5. The height of a triangle with base 12 cm and angle of elevation 30° is _______ cm.

6. The value of cos 0° is _______.

7. If tan A = 3/4, then cot A = _______.

8. The sine of an angle is always between _______ and _______.

9. The sum of the angles in a triangle is always _______ degrees.

10. In a right-angled triangle, the side opposite to the right angle is called the _______.

Practice Questions

1. A person standing 50 meters from a tree sees the angle of elevation to the top of the tree as 45°. What is the height of the tree?

2. If sin A = 0.6, find the value of θ such that A = 30° + θ.

3. Find the length of the opposite side of a triangle if the adjacent side is 9 m and angle A is 60°.

4. What is the value of sec 30°?

5. If the hypotenuse of a right triangle is 15 cm, and one leg is 9 cm, what is the length of the other leg?

6. A ladder 10 meters long is leaning against a vertical wall. If the ladder makes an angle of 60° with the ground, how high up the wall does the ladder reach?

7. Find the value of cos 45° + sin 45°.

8. In a triangle ABC, if angle A = 45°, angle B = 60°, and side c = 10 cm, find the length of side a.

9. What is the value of tan 60° – cot 30°?

10. A tower casts a shadow 40 meters long when the sun’s elevation is 30°. What is the height of the tower?

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