Question

Raina is 1.5 m tall. At an instant, his shadow is 1.8 m long. At the same instant, the shadow of a pole is 9 m long. How tall is the pole?

• A. 6.5 m
• B. 7.5 m
• C. 8.5 m
• D. 6.2 m

Hint:

In problems involving shadows at the same instant, use the concept of similar triangles. Set up a proportion between the height and shadow length to find the unknown.

Answer 1

The Correct Option is B

Step 1: Let the height of the pole be \( h \, \text{m} \).
Step 2: Since both Raina and the pole cast shadows at the same time, the angles of elevation of the Sun are the same for both.
Step 3: This means the triangles formed by Raina and his shadow, and by the pole and its shadow, are similar.
Step 4: Therefore, the ratio of height to shadow length must be equal:
\[ \frac{\text{Height of Raina}}{\text{Shadow of Raina}} = \frac{\text{Height of Pole}}{\text{Shadow of Pole}} \]
Step 5: Substituting the known values:
\[ \frac{1.5}{1.8} = \frac{h}{9} \]
Step 6: Cross-multiply to solve for \( h \):
\[ 1.5 \times 9 = 1.8 \times h \Rightarrow 13.5 = 1.8h \]
Step 7: Divide both sides by 1.8:
\[ h = \frac{13.5}{1.8} = 7.5 \]
\[ \Rightarrow \text{Height of the pole is } \boxed{7.5 \, \text{m}} \]