Answer :
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
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
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
