Question

Solve triangle EFG with the given parts.f = 17.78, F = 27.3°, G = 102.1°

Answer 1

STEP - BY - STEP EXPLANATION

What to find?

g, E and e

Given:

Step 1

Find the measure of side g using the sine ratio.

`\begin{gathered} (sinF)/(f)=(sinG)/(g) \\ \\ (sin27.3)/(17.78)=(sin102.1)/(g) \\ \\ gsin27.3=17.78sin102.1 \\ \\ g=(17.78sin102.1)/(sin27.3) \\ \\ g\approx37.9 \end{gathered}`

Step 2

Find angle E.

`E+F+G=180(sum\text{ of interior angle in a triangle\rparen}`
`\begin{gathered} E+27.3+102.1=180 \\ \\ E=180-102.1-27.3 \\ \\ E=50.6° \end{gathered}`

Step 3

Find side e using the sine ratio.

`\begin{gathered} (sinE)/(e)=(sinF)/(f) \\ \\ (sin50.6)/(e)=(sin27.3)/(17.78) \\ \\ esin27.3=17.78sin50.6 \\ \\ e=(17.78sin50.6)/(sin27.3) \\ \\ e\approx29.96 \end{gathered}`

ANSWER

g=37.9

E=50.6°

e = 29.96