Question

A lamp post stands on a horizontal plane. From a point situated at a distance $150$m from its foot, the angle of elevation of the top is ${30}^o$. What is the height of the lamp post?

• A. $50m$
• B. $50\sqrt{3}m$
• C. $\frac{50}{\sqrt{3}}m$
• D. $100m$

Answer 1

Answer: (B)

$50\sqrt{3}m$

Distance between point of observation and foot of lamp = $150m$

Angle of elevation of top of lamp = ${30}^{\circ }$

Height of lamp $h=AB$

Now from fig $ABC$

the triangle $ABC$ is a right angle triangle

Hence, tan $C=\frac{AB}{BC}$

$AB=150\frac{1}{\sqrt{3}}$

Multiply and divided by $\sqrt{3}$

= $\frac{150\sqrt{3}}{\sqrt{3}\times \sqrt{3}}$

= $\frac{150\sqrt{3}}{3}$

= $50\sqrt{3}m$

the height of the lamp post = $50\sqrt{3}m$.