Height of a tree

Question

A tree shadow casts a shadow that is 53 ft long when the angle of elevation of the sun is 27. Find the height of the tree.

Answer 1

Make a right triangle. The bottom leg is 53 feet you are trying to find the other leg with the angle at the bottom is 27 degrees. If you look at the triangle you

have the opposite side and adjacent side so you have the tangent relationship. Equation is

tan(27) = x/ 53. So x or the height is

c = 53 • tan (27)

make sure your calculator is in degree mode

Answer 2

Hi Sadie:

This is a basic trig problem. Just draw a diagram with a straight line from the sun to the ground at an angle to the ground of 27 degrees. Let the tree height be H and the shadow length is 53'.

The, we have a right angled triangle ABC where A is the top of the tree, B is the base of the tree, and C is the end of the tree's shadow on the ground. Angle ABC = 90 degrees and angle ACB = 27⁰.

By the usual trig ratios: h / 53 = tan (ACB)

=> h = 53 tan 27⁰

= 53 x 0.5095

= 27.00 feet

Answer 3

x = height of tree

tangent (27) = x/53

x = 53 tangent(27) = 27 feet