Question

The length of the shadow of a building is 100 meters, as shown below: the shadow of a building is 100 meters long. the acute angle that the shadow makes with the line joining the tip of the building to the end of the shadow measures 45 degrees. what is the height of the building?

Answer 1

let h = height

tan(45) = h / 100
h = 100tan45
h = 100m

Answer 2

The height of the building whose shadow is making a 45° angle with the ground is 100 meters.

What are Trigonometric functions?

The trigonometric function gives the ratio of different sides of a right-angle triangle.

$\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}$

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.

As we can see in the image below the angle made by the building top with the shadow top is 45°, and the angle between the building and the ground is a right angle, therefore, we can observe that it is forming a right-angled triangle.

Now, as the triangle is a right-angle triangle, therefore, we can apply the trigonometric functions,

$\rm Tan(\theta) = \dfrac{Perpendicular}{Base}$

$\rm Tan(\angle A) = \dfrac{BC}{AB}\\\\\rm Tan(45^o) = \dfrac{BC}{100}\\\\BC = 100\ meter$

Hence, the height of the building is 100 meters.

Learn more about Trigonometric functions:

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