Question

word problems, similar triangles (level 1)
this is the only question in this section.
question
joseph is 1.75 meters tall. at 11 a.m., he measures the length of a trees shadow to be 34.05 meters. he stands 29.7 meters away from the tree, so that the tip of his shadow meets the tip of the trees shadow. find the height of the tree to the nearest hundredth of a meter.
(diagram is not to scale.)

Explanation:

Step1: Find length of Joseph's shadow

The length of Joseph's shadow is $34.05 - 29.7=4.35$ meters.

Step2: Set up proportion

Since the triangles formed by Joseph and his shadow and the tree and its shadow are similar, the ratios of height to shadow - length are equal. Let $h$ be the height of the tree. Then $\frac{h}{34.05}=\frac{1.75}{4.35}$.

Step3: Solve for $h$

Cross - multiply to get $4.35h = 1.75\times34.05$. Then $h=\frac{1.75\times34.05}{4.35}$.
$1.75\times34.05 = 59.5875$.
$h=\frac{59.5875}{4.35}\approx13.698276\approx13.70$ meters.

Answer:

$13.70$ meters