The angle of elevation from me to the top of a hill is 51 degrees. The angle of elevation from me to the top of a tree is 57 degrees. The tree stands 20 ft off the hill. How high is the top of the tree from the base of the hill?

Approximately (assuming that the height of the base of the hill is the same as that of the observer.)

Step-by-step explanation:

Refer to the diagram attached.

Angles:

Let the length of segment (vertical distance between the base of the tree and the base of the hill) be .

The question is asking for the length of segment . Notice that the length of this segment is .

The length of segment could be represented in two ways:

For example, in right triangle , the length of the side opposite to is segment . The length of that segment is .

.

Rearrange to find an expression for the length of (in ) in terms of :

.

Similarly, in right triangle :

.

Equate the right-hand side of these two equations:

.

Solve for :

.

Hence, the height of the top of this tree relative to the base of the hill would be .

4

step-by-step explanation:

im pretty sure it's 4 beacsue 8/2 equals 4