Question

From the top of a light house 30 m high, with its base at the sea level, the angle of depression of a boat is 75°. Find the distance of the boat from the foot of the light house. (in m) ​

Answer 1

Answer:

Height of light house =60 m

Angle of depression = 30∘

Let the distance of boat from the light house = s

Then, angle of depression = angle of elevation

tan∠ of elevation = distanceheight

tan30=s60

s=603 m

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Answer 2

Answer:

The distance of the boat from the bottom of the light house is $8.038m$.

Step-by-step explanation:

It is given that :

The top of the light house is $30m$ high

Base is at sea level

The angle of depression of a boat in the sea is given as $75^0$

Here, we have to find the distance of the boat from the bottom i.e. foot of the light house.

Using trigonometric ratios,

We know that :

$tan \theta=\frac{opposite}{adjacent} \\\\tan 75^0=\frac{30}{x}$

$x=\frac{30}{tan75^0}$

We know that the value of $tan75^0$ is $2 + \sqrt{3} = 3.7321$

Substituting this value in our equation,

$x=\frac{30}{3.7321} \\\\x=8.038$

Hence, the distance of the boat from the bottom of the light house is $8.038m$

Trigonometry:

• The area of mathematics known as trigonometry examines how a triangle's sides and angles relate to one another.
• Trigonometry is a mathematical tool that is frequently used in physics, architecture, and GPS navigation systems.
• It may be used to determine the heights of large mountains or structures and is also used in astronomy to determine the distance between stars or planets.

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