Question

Solve the equation sin(x° − 20°) = cos(42°) for x, where 0 < x < 90.

22
62
68
28

Answer 1

check the picture below.

on the first quadrant, namely 0° < x < 90°, the sine of one acute angle, equals the cosine of the other acute angle, as you see in the example in the picture.

therefore

`\bf sin(90^o-\theta )=cos(\theta )\qquad \boxed{\theta =42}\qquad sin(90^o-42^o )=cos(42^o ) \\\\\\ sin(48^o)=cos(42^o)\\\\ -------------------------------\\\\ sin(\stackrel{48^o}{x^o-20^o})=cos(42^o) \\\\\\ x-20=48\implies x=48+20\implies x=68`