Question

2. As observed from the top of a 60 m height lighthouse from the sea level the angle of depression
of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house. Find the distance between the two ship.
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Answer 1

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As observed from the top of a 60 m height lighthouse from the sea level the angle of depression of two ships are 30° and 45°. If one ship is exactly behind the other on the same side of the light house. Find the distance between the two ship.

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$From \: the \: fig :$

$\purple{\leadsto \: Tan \: 45⁰ = \frac{AB}{BC}}$

$\purple{\leadsto1= \frac{60}{BC}}$

$\purple{\leadsto \: BC= 60}$

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$And,$

$\orange{\leadsto \: Tan \: 30⁰ = \frac{AB}{BE}}$

$\orange{\leadsto\frac{1}{√3} = \frac{60}{BE}}$

$\orange{\leadsto \: BE = 60√3}$

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$\green{\leadsto \: BE - BC = 60√3-60}$

$\green{\leadsto60(√3-1)}$

$\green{\leadsto60(1.732-1)}$

$\green{\leadsto60(0.732)}$

$\green{\leadsto43.92}$

Hence, the distance between two ships is 43.92m.

[Hope this helps you.../]