Chapter 6, Problem 19RE

To determine

The height of the tree.

Answer to Problem 19RE

  $h\approx {31.01}^{\text{'}}$ .

Explanation of Solution

Given information:

A tree stands on a hillside of slope ${28}^o$ from the horizontal. From a point $75$ feet down the hill, the angle of elevation to top of the tree is ${45}^o$ .

  

Calculation:

From the given information, tree stands on a hillside of slope ${28}^o$ from the horizontal. From a point $75$ feet down the hill, the angle of elevation to top of the tree is ${45}^o$ are as shown below:

  

The legs of a ${45}^o-{45}^o-{90}^o$ triangles are equal.

  $h=75\cos {28}^o-75\sin {28}^o=75(\cos {28}^o-\sin {28}^o)\approx {31.01}^{\text{'}}$

Thus, the height of the triangle $h\approx {31.01}^{\text{'}}$ .