If (48° + k) is an acute angle and sin(48° + k) = cos 13°, what is the value of k (in degrees)?

Question

Accepted Answer

Given sin(48° + k) = cos 13° and (48° + k) is an acute angle.

Recall the identity: sin A = cos (90° - A).

So, sin(48° + k) = cos 13° implies:
48° + k = 90° - 13°
48° + k = 77°

Now, solve for k:
k = 77° - 48° = 29°

However, the problem states (48° + k) is an acute angle, which means it must be less than 90°. 77° is less than 90°, so this is valid.

But 29° is not in the options as correct. Let's check the options carefully.

Options are 17, 23, 29, 37.

Our calculation shows k = 29°, which matches option 3.

Therefore, the correct answer is 29°.

Answer

Answer

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