Question

assuming that the two right triangles are similar, find the height of the tower from the given measurements.
(image of two right triangles: left triangle has right angle at r, base rp = 15m; right triangle abc has right angle at b, bc = 3m, ba = 5m)
options:
○ x = 3 m
○ x = 5 m
○ x = 6 m
○ x = 9 m

Explanation:

Step1: Recall Similar Triangles Property

For similar triangles, the ratios of corresponding sides are equal. Let the height of the tower be \( x \) (length of \( QR \)). The small triangle has legs \( 3 \, \text{m} \) ( \( BC \)) and \( 5 \, \text{m} \) ( \( BA \)), and the large triangle has legs \( x \) ( \( QR \)) and \( 15 \, \text{m} \) ( \( RP \)).

Step2: Set Up Proportion

Using the similarity of \( \triangle ABC \) and \( \triangle QRP \), we have \( \frac{BC}{QR} = \frac{BA}{RP} \). Substituting values: \( \frac{3}{x} = \frac{5}{15} \).

Step3: Solve for \( x \)

Cross - multiply: \( 5x = 3\times15 \). So \( 5x = 45 \). Divide both sides by 5: \( x=\frac{45}{5}=9 \).

Answer:

\( x = 9 \, \text{m} \) (the option with \( x = 9 \, \text{m} \))