A man on a deck of a ship 12m above water level observes the angle of elevation of the top - Maths - Some Applications of Trigonometry

Question

A man on a deck of a ship 12m above water level observes
the angle of elevation of the top pf a cliff is 60degree and the
angle of depression of the base of the cliff is 30degree Find the
distance of the cliff from the ship and the height if the
cliff

Lalit Mehra · Accepted Answer

Let AB be the deck of the ship AB = 10 cm Suppose CE be the cliff C and E are the top and bottom of the cliff Let CE = h m Given, âˆ EAD = 60Â° and âˆ DAC = 30Â° CD = AB = 12 m âˆ´ DE = CE â€“ CD = (h â€“ 12) m In Î”ADE, $\tan 60 ° = \frac{DE}{AD} (\tan θ = \frac{Perpenicular}{Base}) ∴ \sqrt{3} = \frac{(h - 12) m}{AD} \Rightarrow AD= \frac{(h - 12)}{\sqrt{3}} m= \frac{(h - 12) \sqrt{3}}{3} m (1)$ In Î”ADC, $\tan 30 ° = \frac{CD}{AD} ∴ \frac{1}{\sqrt{3}} = \frac{12 m}{AD} \Rightarrow AD = 12 \sqrt{3} m (2)$ From (1) and (2), we have $\frac{(h - 12) \sqrt{3}}{3} m=12 \sqrt{3} m ∴ h - 12 = 36 \Rightarrow h = 36 + 12 = 48$ Height of the cliff = 48 m Distance of cliff from the ship = BC = AD = $12 \sqrt{3} m$

A man on a deck of a ship 12m above water level observes the angle of elevation of the top pf a cliff is 60degree and the angle of depression of the base of the cliff is 30degree. Find the distance of the cliff from the ship and the height if the cliff .