P and Q are two points on the ground on either side of a pole. The angles of elevation of the top of the pole as observed from P and Q are 60° and 30°, respectively and the distance between them is 84√3 m. What is the height (in m) of the pole?

Answer: Option B

Solution

Answer: Option B

Solution:

{60^ \circ } = \frac{{\sqrt 3 }}{1}\begin{array}{*{20}{c}} \to &h \\ \to &{\frac{h}{{\sqrt 3 }}} \end{array}
$$PN=\frac{h}{\sqrt{3}}$$
{30^ \circ } = \frac{1}{{\sqrt 3 }}\begin{array}{*{20}{c}} \to &h \\ \to &{\sqrt 3 h} \end{array}
$$\begin{array}{rl}& NQ=\sqrt{3}h\\ & PN+NQ=84\sqrt{3}\\ & \frac{h}{\sqrt{3}}+\sqrt{3}h=84\sqrt{3}\\ & h\left(1+3\right)=84\times \sqrt{3}\times \sqrt{3}\\ & h=\frac{84\times 3}{4}\\ & h=63\text{m}\end{array}$$