Two ships are sailling in the sea on the either side of the lighthouse, the angle of depression of two ships are observed from the top of the light house are $60^{0}$ and $45^{0}$ respectively. if the distance between the ships is $200 (\frac{\sqrt{3} + 1}{\sqrt{3}}) m e t r e s$ , find the the height of the lighthouse.

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Solution

$tan 45^{o} = \frac{h}{A B} A B = h$

$tan 60^{o} = \frac{h}{B C} B C = \frac{h}{\sqrt{3}}$

$A B + B C = (\frac{\sqrt{3} + 1}{\sqrt{3}}) h$

$200 (\frac{\sqrt{3} + 1}{\sqrt{3}}) = (\frac{\sqrt{3} + 1}{\sqrt{3}}) h$

$h = 200$ meters.

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Two ships are sailling in the sea on the either side of the lighthouse, the angle of depression of two ships are observed from the top of the light house are 600 and 450 respectively. if the distance between the ships is 200(√3+1√3)metres, find the the height of the lighthouse.

tan45o=hABAB=htan60o=hBCBC=h√3AB+BC=(√3+1√3)h200(√3+1√3)=(√3+1√3)hh=200 meters.

$tan 45^{o} = \frac{h}{A B} A B = h$

$tan 60^{o} = \frac{h}{B C} B C = \frac{h}{\sqrt{3}}$

$A B + B C = (\frac{\sqrt{3} + 1}{\sqrt{3}}) h$

$200 (\frac{\sqrt{3} + 1}{\sqrt{3}}) = (\frac{\sqrt{3} + 1}{\sqrt{3}}) h$

$h = 200$ meters.