Question

Can someone please help me answer this two part math problem, solve the first triangle then the second

Answer 1

GIVEN

The triangle is shown in the question. The following parameters are given:

$\begin{gathered} \theta=30\degree \\ opp=10 \\ adj=y \\ hyp=x \end{gathered}$

SOLUTION

Recall the sine trig ratio:

$\sin\theta=\frac{opp}{hyp}$

Substitute known values into the ratio:

$\begin{gathered} \sin30=\frac{10}{x} \\ \therefore \\ x=\frac{10}{\sin30} \\ x=20 \end{gathered}$

To solve for y, recall the Pythagorean Theorem:

$hyp^2=opp^2+adj^2$

Substitute known values:

$\begin{gathered} 20^2=10^2+y^2 \\ 400=100+y^2 \\ \therefore \\ y=\sqrt{400-100}=\sqrt{300} \\ y=10\sqrt{3} \end{gathered}$

ANSWER

$\begin{gathered} x=20 \\ y=10\sqrt{3} \end{gathered}$