Question

On a sunny day, a 6-foot tall woman positions herself so that her shadow lines up with the end of the shadow of a pine tree. The woman's shadow is 8 feet long, and she is standing 12 feet from the base of the pine tree, as shown below. Based on the information provided in the diagram, describe how to solve for , the height of the pine tree what's the BE ____ feet Numerical answers only​

Answer 1

Based on the information provided in the diagram, the proportion that can be used to solve for the height of the tree is 4/3 = 24/x, where x the height of the tree is 18 ft.

Two triangles are similar if they have the same shape, but not necessarily the same size. This means that corresponding angles of the two triangles are equal, and corresponding sides are in proportion. Thus by triangle proportionality we have;

8/(8 + 16) = 6/x

8/24 = 6/x

by cross multiplication

8/6 = 24/x

when we simply the left hand side we have

4/3 = 24/x which is same as option H.

x = (3 × 24)/4

x = 18.

Therefore, the proportion that can be used to solve for the height of the tree is 4/3 = 24/x, and the height of the tree x is equal to 18 ft.