Answer:
Step-by-step explanation:
Just for a few minutes we are going to disregard Wendy's 5-foot view above the ground. We'll add it in when we need it; it just causes extra confusion right now. And we're already confused enough, right?
We need to think of this in terms of right triangles. If Wendy is 60 feet from a tree, the base of the right triangle is 60 feet. The height of the tree is the height of the right triangle. The angle of elevation is the one from the ground at her feet to the top of the tree and then to the bird. Let's start with the top of the tree first.
She's 60 feet away, we have the angle of elevation as 25 degrees, and we are looking for the height of the tree. In regards to the angle, the base of 60 is adjacent, and the height of the tree is opposite. The tangent ratio is the one that relates the side opposite to the side adjacent.
[tex]tan(25)=\frac{x}{60}[/tex] where x is the height of the tree. Simplifying,
[tex]60tan(25)=x[/tex] and
x = 27.9 or 28 feet.
But that's from her 5-foot line of vision. Add that 5 feet to the 28 feet and get that the tree is 33 feet tall. Now for the bird.
We have the same base of the triangle as 60, but this time the angle of elevation is 37 degrees, and the height of the bird in the air is y, opposite the angle of elevation (just so you know, this is also called the reference angle). The tangent ratio again relates the side opposite to the side adjacent:
[tex]tan(37)=\frac{y}{60}[/tex] and
[tex]60tan(37)=y[/tex] and
y = 45.2 or 45 feet.
But, again, that's from her 5-foot line of vision. Add that 5 feet to the 45 feet and get that the bird is 50 feet in the air.
To get how far above the tree that the bird is,
50 - 33 = 17 feet
