Question

From the top of a pillar $150$ meters high, the angles of depression of the top and the foot of another pillar are respectively found to be $\theta ,\varphi$. If $\theta =Ta{n}^{-1}\left(\frac{4}{3}\right)$ and $\varphi =Ta{n}^{-1}\left(\frac{5}{2}\right)$. Then the distance between their top is

• A. $50m$
• B. $100m$
• C. $150m$
• D. $200m$

Answer 1

The correct option is B $100m$

Let distance between hillar $\log x$

$\tan \varphi =\frac{150}{x}$

$\frac{5}{2}=\frac{150}{x}\Rightarrow x=60m$

$\tan \theta =\frac{y}{x}$

$\frac{4}{3}=\frac{y}{60}$

$\therefore y=80m$

Distance between tops of hilles $=\sqrt{x^2+y^2}$

$=\sqrt{{60}^2+{80}^2}$

$\sqrt{3600+6400}$

$=\sqrt{10000}$

$=100m$