Consider a triangular plot with sides m, m and m. A vertical lamp-post at the mid-point of subtends an angle at . The height (in m) of the lamp-post is
- A.
- B.
- C.
- D.
Show answer and solution
Correct option: A
Solution
Find BD first using the median formula. D is the midpoint of AC, so BD is a median from B with AB=7, BC=5, AC=6.
BD² = (2·AB² + 2·BC² - AC²)/4 = (2·49 + 2·25 - 36)/4 = (98 + 50 - 36)/4 = 112/4 = 28, so BD = 2√7.
The lamp-post of height h at D subtends 30° at B, meaning tan(30°) = h/BD.
h = BD · tan(30°) = 2√7 · (1/√3) = 2√7/√3 = 2√(7/3) = (2/3)√21.
BD² = (2·AB² + 2·BC² - AC²)/4 = (2·49 + 2·25 - 36)/4 = (98 + 50 - 36)/4 = 112/4 = 28, so BD = 2√7.
The lamp-post of height h at D subtends 30° at B, meaning tan(30°) = h/BD.
h = BD · tan(30°) = 2√7 · (1/√3) = 2√7/√3 = 2√(7/3) = (2/3)√21.
[JEE Main 2019 · 10 Jan · Shift I]