Question

Angles α and β are the two acute angles in a right triangle. Use the relationship between sine and cosine to find the value of β if β < α. sin(3x − 27) = cos(5x + 5)

A) 14°
B) 15°
C) 75°
D) 76°

Answer 1

A) 14°

Explanation:

If α and β are the two angles other than 90° in a right triangle, then we have the relation between α and β as, α+β=90°.

Therefore, Sin α = Sin (90° -β) =Cos β.

So, we can write the reverse as if Sin α = Cosβ, then we have α + β =90°.

It is given that, Sin (3x-27) = Cos (5x+5).

Hence, we can write (3x-27) + (5x + 5) = 90

⇒ 8x = 90+27-5 =112

⇒ x = 14°

Therefore, option A. is correct. (Answer)