Question

jai is 1.45 meters tall. at 11 a.m., he measures the length of a tree’s shadow to be 39.55 meters. he stands 34.1 meters away from the tree, so that the tip of his shadow meets the tip of the tree’s shadow. find the height of the tree to the nearest hundredth of a meter.
(diagram is not to scale.)

Explanation:

Step1: Find Jai's shadow length

The tree's shadow is 39.55 m, and Jai is 34.1 m from the tree. So Jai's shadow length \( s = 39.55 - 34.1 = 5.45 \) m.

Step2: Set up proportion for similar triangles

Let \( h \) be the tree's height. Since the triangles are similar, \( \frac{1.45}{5.45} = \frac{h}{39.55} \).

Step3: Solve for \( h \)

Cross - multiply: \( h=\frac{1.45\times39.55}{5.45} \).
First, calculate \( 1.45\times39.55 = 1.45\times(40 - 0.45)=1.45\times40-1.45\times0.45 = 58 - 0.6525 = 57.3475 \).
Then, \( h=\frac{57.3475}{5.45}\approx10.52 \) (rounded to the nearest hundredth).

Answer:

The height of the tree is approximately 10.52 meters.