Paragraph: $A B C$ is a triangular plot with $A B=16 \mathrm{~m}, B C=10 \mathrm{~m}$ and $C A=10 \mathrm{~m}$. A lamp post is situated at the middle point of the side $A B$. The lamp post subtends an angle $45^{\circ}$ at the vertex $B$.
Question: What is the height of the lamp post?

• A

  6 m
• B

  7 m
• Correct answer
  C

  8 m
• D

  9 m

Solution

$\begin{aligned} & \text { In } \triangle P D B \\ & \tan 45^{\circ}=\frac{P D}{B D} \quad \Rightarrow \quad P D=B D=8 \end{aligned}$ $\therefore \quad$ Height of the lamp post $=8 \mathrm{~m}$

Hence, the correct answer is option: 'C'.