Two vertical poles stand on the ground, 50 meters apart. The height of the smaller pole is 10 meters. From the top of the smaller pole, the angle of elevation of the top of the taller pole is 30°. Find the height of the taller pole.
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Correct answer: B
Explanation
Given:
Distance between two pillars = 50 meters
Height of the shorter pillar = 10 meters
Angle of elevation = 30°
Formula:
tanθ = opposite side / base
Let the height of the taller pillar = h
Difference of heights = h − 10
tanθ = (h − 10) / 50
1/√3 = (h − 10) / 50
h − 10 = 50/√3
h = 10 + 50/√3
h = 10 + 28.87
h = 38.87 meters