Pre Calculus Math Question

After a severe storm, three sisters, April, May and June stood on their front porch and noticed that the tree in their front yard was leaning 7 degrees from vertical toward the house. From the porch, which is 103 feet away from the base of the tree, they noticed that the angle of elevation to the top of the tree was 22 degrees. What is the height of the tree?.

If you change the perspective and draw a sketch of the situation from the side, it should be clear how to solve this.
So
If you have the house on the left and the tree on the right and draw al line from the bottom of the house to the top of the tree, and draw the tree leaning towards the house by an angle of 7 degrees, then you have a simple triangle. One of the base angles is 22 degrees and the other is (90 - 7) = 83 degrees. 22 + 83 = 105 so the third angle is (180 - 105) = 75 degrees. You can now use the Sine law to get the length of the tree.
so
Let length of tree = x ft, then, from the sine law
103 / sin 75 = x / sin 22

x = 103 sin 22 / sin 75 = 39.95 ft

Now drop a vertical line from the top of the tree to the ground to form a right angled triangle.
The height of the top of the tree from the ground is, using the Sine law again,

39.95 / sin 90 = Height / Sin 83
Height = 39.95 Sin 83 / Sin 90 = 39.65 ft above the ground to two decimal places.

As a general tip, make sure you review the Sine law and Cosine law. They crop up again and again especially when doing vector problems.

Draw triangle representing ground, sloping tree and elevated sight line to the top of the tree.
Base AB is 103. A line left from B at 22 degrees from base intersects a line from A, 7 degrees from vertical towards B, at a third point C. Notice that internal angle BAC must be 83 degrees
We assume here that "height of the tree" refers to the altitude h from C to the baseline, not just to the length of the tree.