u are laying on the ground looking up at the sun that appears just over the top of a tree at an angle of elevation of 27°. He is located 32 feet away from the base of the tree. How tall is the tree?

Answer 1

Hi Ellise,

If we picture you lying on the ground on the left side of the picture, and the tree being on the right hand side, then we have a right triangle. The hypotenuse is the line between your eyes and the top of the tree.

When your eyes look up at an angle of 27 degrees, then 32 feet is the adjacent side of the triangle (the side next to you). The height of the tree is the opposite side of the triangle which we’ll call x.

Since we have the opposite and adjacent side we can use the tangent formula:

tangent = opposite / adjacent

tan(27) = x / 32. Multiply both sides by 32:

32 * tan(27) = x

16.3 feet = x

Please let me know if I can be more helpful, thanks!

Joe