Question

PLEASE HELP ASAP

Answer 1

Corey stepped back 59.71 feet to get a better view of the bird.

Explanation:

This is a right angled triangle. Let $\theta$ be the angle of elevation.

Let the adjacent side of the triangle be x for the angle $\theta$

Let the opposite side of the triangle by y for the angle $\theta$

Thus,

$\tan \theta=\frac{y}{x}$

Since, the height of the tree is 80 feet, $y=80$

To find the value of x, let us substitute $y=80$ and $\theta=68$

$x=\frac{80}{\tan 68^{\circ}}=32.32$

Since, Corey moves back a few steps to gain a better view of the bird, the angle of elevation is 41°

Now, we shall find the x for  $y=80$ and $\theta=41$

$x=\frac{80}{\tan 41^{\circ}}=92.03$

To find how many feet Corey step back is to subtract the value of two adjacent sides, thus,

$x=92.03-32.32=59.71$

Thus, Corey stepped back 59.71 feet to get a better view of the bird.