Question

From the top of a rock 50 3m high, the angle of depression of a car on the ground is observed to
be 30°. Find the distance of the car from the rock.​

Answer 1

Answer:

the answer is 150 m

Step-by-step explanation:

angle of depression=angle of elevation=30°

distance of car from rock=x

tan30°=height of rock /distance of car from rock

1/√3=50√3/x

x=150m

Answer 2

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• From the top of a rock 50√3 m high, the angle of depression of a car on the ground is observed to be 30°. Find the distance of the car from the rock.

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Let QR be the distance of the car from the building.

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Now, In △PQR

$\rm tan \: 30 \degree = \frac{PQ}{QR}$

$\rm\implies \: \frac{1}{ \sqrt{3} } = \frac{50 \sqrt{3} }{QR}$

$\rm \implies \: QR = 50 \sqrt{3} \times \sqrt{3}$

$\rm \implies QR = 50 \times 3$

$\rm \implies QR = 150$

∴ Distance of the car from the rock = 150 m.

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★ Some key points About Application of trigonometry:

$\longrightarrow$ The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

$\longrightarrow$ The angle of elevation of an object viewed, is the angle formed by the line of sight with the horizontal when it is above the horizontal level, i.e., the case when we raise our head to look at the object.

$\longrightarrow$ The angle of depression of an object viewed, is the angle formed by the line of sight with the horizontal when it is below the horizontal level, i.e., the case when we lower our head to look at the object.

$\longrightarrow$ The height or length of an object or the distance between two distant objects can be determined with the help of trigonometric ratios.

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