Question

Instructions: Find the measure of the indicated angle to the nearest degree

Answer 1

Answer:

See below.

Step-by-step explanation:

We want to find the unknown angle and we know the sides opposite to it and the hypotenuse. Therefore, we can use sine.

Recall that sine is the ratio of the opposite to the hypotenuse:

$\sin(\theta)=opp/hyp$

Plug in the numbers. The opposite is 20 and the hypotenuse is 55.

$\sin(\theta)=20/55$

Solve for theta (use a calculator):

$\sin(\theta)=20/55\\\theta=\arcsin(4/11)\\\theta\approx21.23\approx21\textdegree$