Chapter 8.4, Problem 5BCYP

To determine

The missing values in the given triangle.

Answer to Problem 5BCYP

  $BC=8.8$

  $AB=4.7$

  $\angle C=28°$

Explanation of Solution

Given:

  

Calculation:

The value of BC will be:

  $\begin{array}{l}\sin 62=\frac{P}{H}\\ \sin 62=\frac{BC}{10}\\ BC=10\left(0.8829\right)\\ BC=8.8\end{array}$

The value of AB will be:

  $\begin{array}{l}\cos 62=\frac{P}{H}\\ \cos 62=\frac{AB}{10}\\ AB=10\left(0.469\right)\\ AB=4.7\end{array}$

The value of $\angle C$ will be:

  $\begin{array}{l}\sin C=\frac{AB}{AC}\\ \angle C={\sin }^{-1}\left(\frac{4.7}{10}\right)\\ \angle C={\sin }^{-1}\left(0.47\right)\\ \angle C=28°\end{array}$