P and Q are two points observed from the top of a building 10 root3 m height. if the angle of depression of thw points are complimentary and PQ is 20m then the distance of P from the building is?
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distance of P from the building is 10 m
Step-by-step explanation:
distance of P from the building = d
Tanα = 10√3/d
Tan (90 - α) = 10√3/(d + 20)
Multiplying both
Tanα * Tan (90 - α) = (10√3/d)(10√3)/(d + 20)
=> Tanα * Cot (α) = 300/(d (d + 20)
=> 1 =300/(d (d + 20)
=> d² + 20d = 300
=> d² + 20d - 300 = 0
=> d² + 30d - 10d - 300 = 0
=> d(d + 30) - 10(d + 30) =0
=> (d - 10)(d + 30) = 0
=> d = 10
distance of P from the building is 10 m
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