Question

Trigonometry help. The instructions don’t make sense to me. Can someone explain this!

Answer 1

Answer: x = 19.42, y = 18.47, z = 18°

Step-by-step explanation:

This is assumed to be a 90° triangle so you can use Soh Cah Toa to answer the questions. You must use a calculator for the last step.

$cos\theta=\dfrac{adjacent}{hypotenuse}\implies cos72^o=\dfrac{6}{x}\implies x=\dfrac{6}{cos72^o}\implies x=19.42\\\\\\tan\theta=\dfrac{opposite}{adjacent}\implies tan72^o=\dfrac{y}{6}\implies y=6\ tan72^o}\implies y=18.47$

Use Triangle Sum Theorem to find the angle measure of z:

90° + 72° + z = 180°

   162°     + z = 180°

                  z = 18°