a person standing between two poles, finds that the subtended at his eyes by the tops of the poles is a right angle. if the height of the poles are two times and four times the height of the person and the distance between the poles is equal to the height of the higher pole, find the ratio of the distances of the person smaller to the bigger poles.
Answers
ratio of the distances of the person smaller to the bigger poles = 3/1 or 1/3
Step-by-step explanation:
Height of person = P
Height of smaller pole = 2P
Height of Larger pole = 4P
Distance between poles = 4P
Let say distance of person from smaller pole = x
and angle subtended = a°
then Distance of person from larger pole = 4P - x
and angle subtended = 90° - a°
Tana° = (2P - P)/x
=>Tana° = P/x
Tan(90° - a°) = (4P - P)/(4P - x)
=> Cota° = 3P/(4P - x)
Tana° * Cota° = 1
=> (P/x) * 3P/(4P - x) = 1
=> 3P² = 4Px - x²
=> x² - 4Px + 3P² = 0
=> x² - Px - 3Px + 3P² = 0
=> x(x - P) - 3P(x - P) = 0
=> (x - 3P)(x - P) = 0
=> x = 3P or x = P
x/(4P-x) = 3P/(4P -3P) or P/(4P P)
= 3/1 or 1/3
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