Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 Degree and 45 Degree respectively. If the lighthouse is 100 m high, the distance between the two ship
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Let AB be the lighthouse and C and D be the positions of the ships.
\begin{aligned}
\text{AB = 100m}, \angle{ACB}=30^{\circ}, \\
\angle{ADB}=45^{\circ}\\
\frac{AB}{AC} = tan&30{\circ} = \frac{1}{\sqrt{3}} \\
=> AC = AB*\sqrt{3} = 100\sqrt{3}m\\
\frac{AB}{AD} = tan&45^{\circ} = 1 \\
=> AB = AD = 100m\\
CD = AC+AD\\
= (100\sqrt{3}+100)&m \\
= 100(\sqrt{3}+1)&m\\
= 100*2.73&m
= 273m
\begin{aligned}
\text{AB = 100m}, \angle{ACB}=30^{\circ}, \\
\angle{ADB}=45^{\circ}\\
\frac{AB}{AC} = tan&30{\circ} = \frac{1}{\sqrt{3}} \\
=> AC = AB*\sqrt{3} = 100\sqrt{3}m\\
\frac{AB}{AD} = tan&45^{\circ} = 1 \\
=> AB = AD = 100m\\
CD = AC+AD\\
= (100\sqrt{3}+100)&m \\
= 100(\sqrt{3}+1)&m\\
= 100*2.73&m
= 273m
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