Chapter 8.5, Problem 38SPR

To determine

To calculate:

The height of the tree

Answer to Problem 38SPR

The height of tree is $23ft$ .

Explanation of Solution

Given information:

  

Calculation:

  

In ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle, $l$ are congruent and the length of hypotenuse $h$ is $\sqrt{2}$ times the length.

Acute angles of the right triangle are complementary, so the measure of third angle is

  $90-45=45$

This is ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle. Since, ${45}^{\circ }-{45}^{\circ }-{90}^{\circ }$ triangle has congruent sides, Tree net height is equal to the horizontal distance that is $6yd$ .

By using the conversion factor $\frac{3ft}{1yd}$ to rewrite as $6yd$ :

  $\begin{array}{l}6yd=6yd\times \frac{3ft}{1yd}\\ 6yd=18ft\end{array}$

The height of tree is $18+5=23ft$ .