Chapter 8.6, Problem 6WE

To determine

To find: The value of the variables x and y.

Answer to Problem 6WE

  $x=28,y=25$

Explanation of Solution

Given information:

Calculation:

Since the triangle is isosceles, the median bisects the base.

Using Trigonometric ratio,

  $\begin{array}{l}\cos 65°=\frac{12}{x}\\ \Rightarrow x=\frac{12}{\cos 65°}\\ \Rightarrow x\approx \frac{12}{.4226}\\ \Rightarrow x\approx 28.39\text{ or }28\end{array}$

Thus, $x=28$

Again, using Trigonometric ratio,

  $\begin{array}{l}\sin 65°=\frac{y}{28}\\ \Rightarrow y=28\times (\sin 65°)\\ \Rightarrow y\approx 28\times .9063\\ \Rightarrow y\approx 25.37\text{ or 25}\end{array}$

Thus, $y=25$