Question

A man standing on the deck of a ship, which is 10 m above the water level, observes the angle of elevation of the top of a hill as 60°, and the angle of depression of the base of the hill as 30°. Find the distance of
the hill from the ship and the height of the hill. ​

Answer 1

➝ Given :-

→ Angle of elevation of the top of the hill = 60°

→ Angle of depression of the base of the hill = 30°

→ AB = 10cm

➝ To find :-

→ the distance of the hill from the ship and the height of the hill

Solution :-

Let AB be the deck and CD be the hill

Let the man be at B.

→ AB = 10 m

→ Let BE ⊥ CD and AC ⊥ CD

→ Then, ∠EBD = 60° and ∠EBC = 30°

→ ∠ACB = ∠EBC = 30°,

→ Let CD =h metres.

→ CE = AB = 10 m and

→ ED =(h-10) m

From right ∆CAB, we have

$\frac{AC}{AB} = \cot30° = \sqrt{3} \\ \frac{AC}{10m} = \sqrt{3} \\ AC = 10 \sqrt{3} m \\ BE = AC = 10 \sqrt{3} m \\ from \: right \: BED \: we \: have \\ \frac{DE}{BE} = tan {60}^{0} = \sqrt{3} = \frac{h - 10}{10 \sqrt{3} } = \sqrt{3}$

→ h-10 = 30

→ h = 40m

hence the distance of the ship from the hill is 10√3m and the height of the hill is 40m.

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Note :-

Refer the above attachment