Question

connor is 1.55 meters tall. at 1 p.m., he measures the length of a trees shadow to be 39.75 meters. he stands 34.7 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.

Explanation:

Step1: Find Connor's shadow length

Let Connor's shadow length be \( x \). The tree's shadow is 39.75 m, and Connor is 34.7 m from the tree, so \( x + 34.7 = 39.75 \). Solving for \( x \): \( x = 39.75 - 34.7 = 5.05 \) m.

Step2: Set up proportion for similar triangles

Let the tree's height be \( h \). Since the triangles (Connor and his shadow, tree and its shadow) are similar, \( \frac{h}{39.75}=\frac{1.55}{5.05} \).

Step3: Solve for \( h \)

Multiply both sides by 39.75: \( h=\frac{1.55\times39.75}{5.05} \). Calculate numerator: \( 1.55\times39.75 = 61.6125 \). Then \( h=\frac{61.6125}{5.05}\approx12.20 \) m.

Answer:

The height of the tree is approximately \( 12.20 \) meters.