Question

A hiker whose eyes are 5.5 feet above the ground stands 25 feet from the base of a redwood tree. She looks up at an angle of 71 degrees to see the top of the tree. To the nearest tenth of a foot, what is the height of the tree?

Answer 1

Tan of a 71 degree angle = 71 tan/1=72 feet + 5.5 feet (because of the height of the hiker's eyes) = 78.1 feet

Answer 2

If you draw out a diagram of the situation, the height of the person is 5.5 feet, standing 25 feet away from the tree. then the person looks up at a 71 degree angle with the top of the tree, it should look like a right triangle on top of a rectangle. 

We know the angle she's looking at (71 degrees) and the side adjacent to the angle (the distance she is away from the tree, 25 feet). Using tangent we can solve for the opposite side. 

tan(71 degrees) = x ÷ 25
25 tan (71 degrees) = x
x is about 72.6 feet 

that's the height from her eyes to the top of the tree. 
To get the height of the tree you add how high above the ground her eyes are (5.5 feet) to x (72.6 feet) 

72.6 + 5.5 = 78.1 feet

that should be the height of the tree