Corey spies a bald eagle in a tall tree. He estimates the height of the tree to be 60 feet and the angle of elevation to the bird from where he stands to be 64°. The leaves on the tree make it difficult for Corey to watch the bird, so he takes many steps away from the tree to get a better view. He now estimates his angle of elevation to be 37°. How many feet did Corey step back to gain a better view of the bird? Round your answer to the nearest hundredth of a foot.

Corey stepped back 59.71 feet

Step-by-step explanation:

Right Triangles

They are a special type of triangle where one of its internal angles is 90°. The basic trigonometric equations stand in this type of triangles. If x is the adjacent leg of a given angle , and y is the opposite leg to the same angle, then :

We can solve for x to get

Corey estimates the height of the tree to be 80 feet. This means we know y=80 and . Let's find the horizontal distance at which Corey is looking at the bald eagle:

Now Corey moves back to watch the very same tree at an elevation angle of 41°. The tree has the same height, so

Now we can know the distance Corey walked back by subtracting both distances

correy stepped back 59.71 feet

the 3rd option is right

step-by-step explanation:

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.