JEE Main 2019 Mathematics question on Trigonometry
Two vertical poles of heights, 20 m and 80 m stand apart on a horizontal plane. The height (in m) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is
A.
15
B.
16
C.
12
D.
18
Show answer and solution
Correct option: B
Solution
Using the formula for the height of intersection: h = (h₁ × h₂)/(h₁ + h₂) = (20 × 80)/(20 + 80) = 1600/100 = 16 m. This harmonic mean formula comes from setting up similar triangles — if the poles are distance d apart, the intersection height satisfies 1/h = 1/h₁ + 1/h₂, giving h = 16 m regardless of the horizontal distance between the poles.
[JEE Main 2019 · 8 Apr · Shift II]
Practise Trigonometry the way it is asked
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