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Question (31)

QN0036851

31. If sin A = cos A, where A is acute, then A is:

(A) 30°
(B) 45°
(C) 60°
(D) 90°

Correct Answer: B

Explanation:

Sine and cosine are equal at 45°.

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Question (32)

QN0036852

32. If A + B = 90°, which relation is necessarily true?

(A) sin A = sin B
(B) cos A = cos B
(C) sin A = cos B
(D) tan A = tan B

Correct Answer: C

Explanation:

A and B are complementary angles, so sin A = cos B.

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Question (33)

QN0036853

33. In a right triangle, if one acute angle is 35°, the other acute angle is:

(A) 45°
(B) 50°
(C) 55°
(D) 65°

Correct Answer: C

Explanation:

The two acute angles of a right triangle add up to 90°. Therefore, the other angle is 90° − 35° = 55°.

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Question (34)

QN0036854

34. In a right triangle, the hypotenuse is 25 cm and the side opposite angle A is 7 cm. Then sin A is:

(A) 7/18
(B) 7/25
(C) 24/25
(D) 18/25

Correct Answer: B

Explanation:

sin A = opposite/hypotenuse = 7/25.

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Question (35)

QN0036855

35. A right triangle has perpendicular sides 9 cm and 12 cm. For the angle opposite the side of length 9 cm, tan A is:

(A) 3/4
(B) 4/3
(C) 3/5
(D) 4/5

Correct Answer: A

Explanation:

tan A = opposite/adjacent = 9/12 = 3/4.

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Question (36)

QN0036856

36. A right triangle has hypotenuse 13 cm and one leg 5 cm. For the angle opposite the 5 cm side, cos A is:

(A) 5/13
(B) 12/13
(C) 5/12
(D) 13/12

Correct Answer: B

Explanation:

By Pythagoras, the other leg is 12 cm. Hence cos A = 12/13.

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Question (37)

QN0036857

37. If tan A = 1/√3, then sin A + cos A is:

(A) (√3 + 1)/2
(B) (√3 − 1)/2
(C) 1/2
(D) 1

Correct Answer: A

Explanation:

A = 30°. Thus sin A + cos A = 1/2 + √3/2 = (√3 + 1)/2.

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Question (38)

QN0036858

38. If tan A = √3, then sin A cos A is:

(A) 1/2
(B) √3/4
(C) 3/4
(D) √3/2

Correct Answer: B

Explanation:

A = 60°. Hence sin A cos A = (√3/2)(1/2) = √3/4.

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Question (39)

QN0036859

39. If sin A = 3/5, then (1 − sin A)/(1 + sin A) is:

(A) 1/4
(B) 1/5
(C) 1/2
(D) 2/5

Correct Answer: A

Explanation:

(1 − 3/5)/(1 + 3/5) = (2/5)/(8/5) = 1/4.

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Question (40)

QN0036860

40. If cos A = 3/5, then (1 − cos A)/(1 + cos A) equals:

(A) 1/4
(B) 1/2
(C) 1/5
(D) 3/5

Correct Answer: A

Explanation:

(1 − 3/5)/(1 + 3/5) = (2/5)/(8/5) = 1/4.

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Question (31)

31. If sin A = cos A, where A is acute, then A is:

Explanation:

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Question (32)

32. If A + B = 90°, which relation is necessarily true?

Explanation:

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Question (33)

33. In a right triangle, if one acute angle is 35°, the other acute angle is:

Explanation:

Link:

Question (34)

34. In a right triangle, the hypotenuse is 25 cm and the side opposite angle A is 7 cm. Then sin A is:

Explanation:

Link:

Question (35)

35. A right triangle has perpendicular sides 9 cm and 12 cm. For the angle opposite the side of length 9 cm, tan A is:

Explanation:

Link:

Question (36)

36. A right triangle has hypotenuse 13 cm and one leg 5 cm. For the angle opposite the 5 cm side, cos A is:

Explanation:

Link:

Question (37)

37. If tan A = 1/√3, then sin A + cos A is:

Explanation:

Link:

Question (38)

38. If tan A = √3, then sin A cos A is:

Explanation:

Link:

Question (39)

39. If sin A = 3/5, then (1 − sin A)/(1 + sin A) is:

Explanation:

Link:

Question (40)

40. If cos A = 3/5, then (1 − cos A)/(1 + cos A) equals:

Explanation:

Link:

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