Question

Joseph's math teacher challenges him to estimate the height of a pine tree next to the school. Joseph walks 9.9 meters from the base of the trunk, lies on his belly, and measures a 45° angle of elevation to the top of the tree. What is Joseph trying to calculate?

A. The height of the pine tree
B. The distance to the school
C. The tree's age
D. The width of the tree trunk

Answer 1

Joseph is trying to calculate the height of the pine tree.

Step-by-step explanation:

Joseph is trying to calculate the height of the pine tree.

To calculate the height, Joseph measures the angle of elevation to the top of the tree, which is 45 degrees.

Then, using basic trigonometry, he can use the tangent function to find the height of the tree. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the height of the tree is the opposite side and the distance from Joseph to the base of the tree is the adjacent side. So, Joseph can use the formula:

Height of the tree = Distance from Joseph to the base of the tree x Tangent(45 degrees)