Question

In a right triangle, Sin (30 + x) º = Cos (3x) º. What is the value of x?

Answer 1

`x=15^\circ`

Explanation:

In a right triangle:

`\sin \theta =cos(90^\circ-\theta) $ (Complementary angles)`

Therefore, given:

`Sin (30 + x) \º = Cos (3x) \º\\30+x+3x=90^\circ\\30+4x=90^\circ\\4x=90^\circ-30^\circ\\4x=60^\circ\\$Divide both sides by 4\\x=15^\circ`