Question

1. sonya is 66 inches tall. she wants to estimate the height of a palm tree near her school. she measures her shadow and the palm tree’s shadow. she then makes a sketch as shown below.

image of palm tree with shadow 10 ft, sonya with shadow 2 ft and height 5 ft 6 in

which of these is the best estimate of the height of the palm tree?
hint: 1 ft = 12 in.

options:

• 20 ft
• 27.5 ft
• 13.5 ft
• 3.6 ft

clear all

Explanation:

Step1: Convert Sonya's height to feet

Sonya's height is 66 inches. Since \( 1 \text{ ft} = 12 \text{ in} \), we divide 66 by 12: \( \frac{66}{12} = 5.5 \text{ ft} \).

Step2: Set up proportion for similar triangles

Let \( h \) be the height of the palm tree. The ratio of height to shadow length should be equal for Sonya and the palm tree. So, \( \frac{5.5}{2} = \frac{h}{10} \).

Step3: Solve for \( h \)

Cross - multiply: \( 2h = 5.5\times10 \). Then \( 2h = 55 \), and \( h=\frac{55}{2}=27.5 \text{ ft} \).

Answer:

27.5 ft (the option with 27.5 ft)