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Q.

If $sin A = 34$ , what is the value of cos A?

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a

74

b

72

c

79

d

78

answer is A.

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Detailed Solution

Given that,

sin A = 34

.
Sine is a ratio of the side opposite to angle A to the hypotenuse. If k is any positive integer,

sin A = 3 k 4 k ⇒ opposite side H y p o t e n u s e = 3 k 4 k

Form a triangle with respect to A with opposite side as BC and hypotenuse AC.
Question Image

Question Image

Applying Pythagoras theorem,

A C 2 = B C 2 + A B 2 ⇒ 16 k 2 = 9 k 2 + A B 2 ⇒ A B 2 = 16 k 2 − 9 k 2 ⇒ A B 2 = 7 k 2 ⇒ A B = 7 k

cos A = A d j a c e n t side H y p o t e n u s e ⇒ cos A = 7 k 4 k ⇒ cos A = 74

So, the value of cos A is

74

.
Hence, option 3 is correct.

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If sinA= 3 4 , what is the value of cos A?