Chapter 8.4, Problem 5ACYP

To determine

The missing values in the given triangle.

Answer to Problem 5ACYP

  $FH=12$

  $\angle G=67°$

  $\angle F=23°$

Explanation of Solution

Given:

  

Calculation:

According to the Pythagorean Theorem,

  $\begin{array}{l}{\left(FH\right)}^2+{\left(GH\right)}^2={\left(FG\right)}^2\\ {\left(FH\right)}^2+{\left(5\right)}^2={\left(13\right)}^2\\ {\left(FH\right)}^2=169-25\\ FH=12\end{array}$

The value of $\angle F$ will be:

  $\begin{array}{l}\sin F=\frac{5}{13}\\ \angle F={\sin }^{-1}\left(0.384\right)\\ \angle F=23°\end{array}$

The value of $\angle G$ will be:

  $\begin{array}{l}\sin G=\frac{12}{13}\\ \angle G={\sin }^{-1}\left(0.923\right)\\ \angle G=67°\end{array}$