Question

Solve the following non-right triangles. a. A= 37°, C= 75° , a= 11

Answer 1

To solve the given triangle:

1. Find the missing angle (angle B)

The sum of internal angles of a triangle is always 180°:

`\begin{gathered} A+B+C=180 \\ B=180-A-C \\ \\ B=180-37-75 \\ B=68 \end{gathered}`

2. Use sine law to find the b and c:

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

Find b:

`\begin{gathered} (b)/(\sin B)=(a)/(\sin A) \\ \\ b=(a\cdot\sin B)/(\sin A) \\ \\ b=(11\cdot\sin68)/(\sin37)=16.94 \end{gathered}`

Find c:

`\begin{gathered} (c)/(\sin C)=(a)/(\sin A) \\ \\ c=(a\cdot\sin C)/(\sin A) \\ \\ c=(11\sin 75)/(\sin 37)=17.65 \end{gathered}`