Question 9.2E3: Using Similar Triangles to Find the Height of a Tree Monique......
Using Similar Triangles to Find the Height of a Tree
Monique Currie plans to remove a tree from her backyard. She needs to know the height of the tree. Monique is 6 ft tall and determines that when her shadow is 9 ft long, the shadow of the tree is 45 ft long (see Fig. 9.22 on page 494). How tall is the tree?
We will let x represent the height of the tree. From Fig. 9.22, we can see that the triangle formed by the sun’s rays, Monique, and her shadow is similar to the triangle formed by the sun’s rays, the tree, and its shadow. To find the height of the tree, we will set up and solve the following proportion:
\frac{\text{height of the tree}}{\text{height of Monique}} = \frac{\text{length of tree’s shadow}}{\text{length of Monique’s shadow}}
\frac{x}{6} = \frac{45}{9}
9x = 270
x = 30
Therefore, the tree is 30 ft tall.