If ( 48^° + k ) is an acute angle and sin( 48^° + k ) = cos13^° , what is the value of k(in ^° )?

If ( 48^° + k ) is an acute angle and sin( 48^° + k ) =…

If ( $48^\circ + k$ ) is an acute angle and sin( $48^\circ + k$ ) = $\cos13^\circ$ , what is the value of k(in $^\circ$ )?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. 29.

sin(x) = cos(90° - x)

Now, sin (48° + k) = cos 13°

⇒ sin (48° + k) = sin (90° - 13°)

⇒ 48° + k = 90° - 13°

⇒ k = 90° - 13° - 48° = 29°

Therefore, the value of k is 29°.