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=(opp)/(hyp)`

Substitute known values into the ratio:

`\begin{gathered} \sin30=(10)/(x) \\ \therefore \\ x=(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=√(400-100)=√(300) \\ y=10√(3) \end{gathered}`

ANSWER

`\begin{gathered} x=20 \\ y=10√(3) \end{gathered}`