Question

A man stranding on the deck of the ship which is 20 m above the sea level , observes the angle of elevation of a bird as 30° and the angle of depression of its reflection in the sea as 60°. find the height of the bird.

Answer 1

$\textbf {Hey there, here is the solution.}$

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STEP 1: Find the horizontal distance from the man to the bird:

Angle of depression = 60°

Vertical height from the sea level to the deck = 20m

$\tan(\theta) = \dfrac{\text{opposite}}{\text{adjacent}}$

$\tan(60) = \dfrac{\text{20}}{\text{distance}}$

$\text {distance} = \dfrac{20}{\tan(60) }$

$\text {distance} = 11.55 \text { m}$

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STEP 2: Find the vertical height from the deck to the height of the bird:

Angle of elevation = 30°

$\tan(\theta) = \dfrac{\text{opposite}}{\text{adjacent}}$

$\tan(30) = \dfrac{\text{height}}{11.55}$

$\text {height} = \tan(30) \times 11.55$

$\text {height} = 6.67 \text { m}$

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STEP 3: Find the height of the bird from the sea level:

Height = 11.55 + 6.67 = 18.22 m

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Answer: The height of the bird is 18.22 m.

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$\textbf {Cheers}$