Question

a) 14° b) 34° c) 56° d) 224°

1. the angle of the roof on kayas dollhouse is 56°. she built a scale model of the dollhouse with a scale ratio of 1:4. what is the measure of the angle of the roof of the model?
2. a six - foot - tall person is standing next to a flagpole. the person is casting a shadow 1 1/2 feet in length, while the flagpole is casting a shadow 5 feet in length. how tall is the flagpole?

a) 30 ft b) 25 ft c) 20 ft d) 15 ft
a) de/pq = 6/4 b) pq/de = 6/4 c) pq/ef = 4/9 d) pr/de = 6/6

Explanation:

Step1: Set up proportion

Since the person and the flagpole form similar triangles (because the sun's rays are parallel, creating equal angles), we can set up a proportion. Let \( h \) be the height of the flagpole. The ratio of height to shadow length is the same for both the person and the flagpole. So, \(\frac{\text{Person's height}}{\text{Person's shadow}}=\frac{\text{Flagpole's height}}{\text{Flagpole's shadow}}\).
Given the person's height is \( 6 \) feet, the person's shadow is \( 1\frac{1}{2}=\frac{3}{2} \) feet, and the flagpole's shadow is \( 5 \) feet. The proportion is \(\frac{6}{\frac{3}{2}}=\frac{h}{5}\).

Step2: Cross - multiply

Cross - multiplying gives us \( \frac{3}{2}h = 6\times5\).
Simplify the right - hand side: \(6\times5 = 30\), so the equation is \(\frac{3}{2}h=30\).

Step3: Solve for \(h\)

Multiply both sides of the equation by \(\frac{2}{3}\) to isolate \(h\). \(h = 30\times\frac{2}{3}\).
Calculate \(30\times\frac{2}{3}\): \(30\div3\times2=10\times 2 = 20\).

Answer:

\(20\) ft (Option c)