a man standing on tyhe deck of a ship which is 10 m above the wateer level he observes - Maths - Some Applications of Trigonometry

Question

a man standing on tyhe deck of a ship which is 10 m above the
wateer level he observes the angle of elevation of the top of a
hill as 60 degree and the angle of depression of the base of the
hill as 30 degree calculate the distanc3e of the hill from the ship
and the height of the hill

Priyanka Kedia · Accepted Answer

Let B be man, D the base of the hill, x be the distance of hill from the ship and h+10 be the height of the hill.

$∠ A B C = 60^{0}, ∠ D B C = 30^{0} I n Δ A C B, \tan 60^{0} = \frac{A C}{B C} \Rightarrow \sqrt{3} = \frac{h}{x} \Rightarrow h = x \sqrt{3} ...... (1) I n Δ B C D, \tan 30^{0} = \frac{C D}{B C} \Rightarrow \frac{1}{\sqrt{3}} = \frac{10}{x} \Rightarrow x = 10 \sqrt{3} ...... (2)$

Substitute the value of x from equation (2) into equation (1), we have,

$h = (10 \sqrt{3}) \sqrt{3} = 10 \times 3 = 30 m$

So,

Height of the hill = h +10 =30 +10 =40 m

And, distance of the hill from the ship is $10 \sqrt{3} m$ .

a man standing on tyhe deck of a ship which is 10 m above the wateer level .he observes the angle of elevation of the top of a hill as 60 degree and the angle of depression of the base of the hill as 30 degree . calculate the distanc3e of the hill from the ship and the height of the hill.