Question

Solve the triangle, find m

Answer 1

The triangle is a right-angle triangle with two sides given.

To find angle A, we Apply trigonometry ratios cosine

`\begin{gathered} \cos A=(adjacent)/(Hypothenuse) \\ \text{Adjacent}=17,\text{Hypothenuse}=38 \end{gathered}`

Substitute the parameters into the formula

`\begin{gathered} CosA=(17)/(38) \\ CosA=0.4474 \\ A=\cos ^(-1)(0.4474) \\ A=63.42^0 \end{gathered}`

Then the measure of A=63° to the nearest degree

To find Angle B, we apply the trigonometry ratio for sine

`\begin{gathered} \text{ Recall that} \\ \sin C=(opposite)/(Hypothenuse) \\ \text{opposite}=17,\text{Hypothenuse}=38 \end{gathered}`

Substitute the parameters into the formula above

`\begin{gathered} \text{sinC}=(17)/(38) \\ \sin C=0.4474 \\ C=\sin ^(-1)(0.4474) \\ C=26.58 \end{gathered}`

Then, the measure of C=27° to the nearest degree

Therefore A=63° and c=27°