First slide

Applications of trigonometry

Question

Two vertical poles AB = 15 m and CD = 10 m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is :

Moderate

A

6
B

10/3
C

5
D

20/3

Solution

$\begin{array}{l} Δ CPQ ~ Δ CBA \\ \frac{y}{x + y} = \frac{h}{15} \\ Δ APQ ~ Δ ADC \\ \frac{x}{x + y} = \frac{h}{10} \\ (1) + (2) 1 = \frac{h}{15} + \frac{h}{10} \\ h (\frac{2 + 3}{30}) = 1 \Rightarrow h = 6 \end{array}$

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