An aeroplane at an altitude of 1500m find that two ship are sailding towards it in the same direction. The angle of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ship.
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Let D is the aeroplane A and B are two ships.
Given: CD=1500 m,∠EDA=30°,∠EDB=45°
In △DBC tan45° = DC/BC
= 1500/BC
1= 1500/BC
⇒BC = 1500 m
In △ADC tan30°= DC/AC
1/√3 = 1500/AB+BC
AB+BC = 1500√3
AB = 1500√3 - 1500
AB = 1500 (√3 - 1)
AB = 1500 (1.73 - 1)
AB = 1500×0.73 = 1095 m
Hence, distance between two ships is 1095 m.
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