Question

Find the value for θ.

sin θ = cos(θ−18.5)
Question 6

35.75°


71.5°


54.25°


161.5°

Answer 1

Answer:

$\theta=54.25\°$

Step-by-step explanation:

we know that

When the sine of angle X is equal to the cosine of angle Y, then angle X and angle Y are complementary angles

so

$X+Y=90\°$----> equation A

In this problem

$X=\theta$

$Y=(\theta-18.5)$

substitute in the equation A

$\theta\°+(\theta-18.5)\°=90\°$

$2\theta=90+18.5$

$2\theta=108.5$

$\theta=54.25\°$