Question

from the top of a building an observer look at a car on the road and find the angle of depression 30 degree.if the height of the building is 45 metre, find how far is the car from building
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Answer 1

Answer:

$\bigstar{\bold{Distance\:=\:45\sqrt{3} \:m}}$

Step-by-step explanation:

$\Large{\underline{\underline{\it{Given:}}}}$

• Angle of depression = 30°
• Height of the building = 45 m

$\Large{\underline{\underline{\it{To\:Find:}}}}$

• The distance of car from the building

$\Large{\underline{\underline{\it{Solution:}}}}$

↠ From the given figure in the attatchment, AB= height of the building = 45 m, Angle C = 30°

↠ We need to find BC which is the distance from car to the building.

↠ tan C = opposite/ adjacent

    tan C = AB/ BC

    tan C = 45/BC

    tan 30° = 45/BC

     $\dfrac{1}{\sqrt{3} } \:=\:\dfrac{45}{BC}$

    BC = 45√3 m

$\boxed{\bold{Distance\:=\:45\sqrt{3} \: m}}$

$\Large{\underline{\underline{\it{Notes:}}}}$

↬ Sin A  = opposite/hypotenuse

↬ Cos A = adjacent/hypotenuse

↬ Tan A = opposite/ adjacent