Question

question 29 of 40
the figure shows a child estimating the height of a tree by looking at the of the tree with a mirror. assuming that both the child and the tree form angles with the ground, which of the following proportions can be used to estimate the height of the tree?
4 ft
5 ft 12 ft
a. $\frac{h}{12}=\frac{5}{4}$
b. $\frac{h}{5}=\frac{4}{12}$
c. $\frac{h}{5}=\frac{12}{4}$
d. $\frac{h}{4}=\frac{12}{5}$

Explanation:

Step1: Identify similar - triangles

The two right - angled triangles formed by the child, the mirror, and the tree are similar. For similar triangles, the ratios of corresponding sides are equal.

Step2: Set up the proportion

The height of the child is 4 ft, the distance of the child from the mirror is 5 ft, and the distance of the tree from the mirror is 12 ft. Let the height of the tree be \(h\). The ratio of the height of the tree to the distance of the tree from the mirror should be equal to the ratio of the height of the child to the distance of the child from the mirror. So, \(\frac{h}{12}=\frac{4}{5}\), which can be rewritten as \(\frac{h}{4}=\frac{12}{5}\).

Answer:

D. \(\frac{h}{4}=\frac{12}{5}\)