What is the height of the lamp post?

Consider the following for the next three (03) items that follow : ABC is a triangular plot with AB=16~m, BC = 10~m and CA=10~m. A lamp post is situated at the middle point of the side AB. The lamp post subtends an angle 45^\circ at the vertex B.

  1. A. 6 m
  2. B. 7 m
  3. C. 8 m ✓
  4. D. 9 m

Correct Answer: C. 8 m

Explanation

Let M be the midpoint of AB, so MB = 16/2 = 8 m. Let h be the height of the lamp post at M. The right-angled triangle formed by the lamp post and point B has angle 45^\circ at B. Thus, \tan 45^\circ = \frac{h}{MB} \implies 1 = \frac{h}{8}, which gives h = 8 m.

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