Question

Please show me how to solve this triangle, thank you!

Answer 1

Statement Problem: Solve for the missing sides of the triangle;

Solution:

The sum of angles in a triangle is 180degrees. Thus,

`\begin{gathered} \angle A+\angle B+\angle C=180^o \\ \angle B=180^o-\angle A-\angle C \\ \angle B=180^o-42^o-96^o \\ \angle B=42^o \end{gathered}`

Since measure angle A and measure angle B are equal. Thus, the triangle is isosceles and the two sides are equal.

`a=b`

We would apply sine rule to find the missing side a.

`\begin{gathered} (\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c) \\ (\sin A)/(a)=(\sin C)/(c) \end{gathered}`
`\begin{gathered} (\sin42^o)/(a)=(\sin96^o)/(12) \\ a=(12\sin42^o)/(\sin96^o) \\ a=8.07 \\ a\approx8.1 \end{gathered}`

Thus,

`a=b=8.1`

CORRECT ANSWERS:

`\begin{gathered} a=8.1 \\ b=8.1 \\ m\angle B=42^o \end{gathered}`