a man standing on a deck of a ship 8m above the water level . he observed that the angle of elevation off the top of the Hill is 60 degree and the angle of depression of the base of the Hill is 30 degree calculate the distance of the hill from the ship and height of the hill.
Answers
Answer:
Step-by-step explanation:
Answer:
Distance of Hill from the Ship (L) = 13.86 m, Height of the Hill (H) = 32 m
Step-by-step explanation:
Given:
(Please see the attached figure for reference)
Let the height of the point where man is standing above water level be (h1)
h1 = 8 m
Height of the elevation of the top of the hill = h2
Distance between Hill and the ship = L
Angel of elevation = 60°
Angel of depression = 30°
Answer:
From trigonometric equation we know that
Tan ∅ = (Length of opposite side / Length of adjacent side)
Thus for the triangle of depression, we get
Tan 30° = (h1) / L
Substituting the values we get
0.577 = 8 / L
∴ L = 8/0.577
∴ L = 13.86 m .......... (1) Distance of Hill from the Ship
Applying trigonometric equation to the triangle of elevation..
Tan 60° = h2 / L
Substituting the values, we get
1.732 = h2 / 13.86
∴ h2 = 1.732 x 13.86
∴ h2 = 24 m ..................(2) Height of elevation
Total height of the hill = h1 + h2
∴ H = 8 + 24
∴ H = 32 m ..... (3) .... Height of the hill
Therefore,
Distance of Hill from the Ship (L) = 13.86 m,
Height of the Hill (H) = 32 m
