Question

The length of a shadow of a building is 31 meters. The distance from the top of the building to the tip of the shadow is 35 meters. Find the height of the building

Answer 1

Answer:

Height of the building is 16.25 meters.

Step-by-step explanation:

We are attaching the diagram for your reference.

Let A be the top of the building, point b represents tip of the shadow and point C is the bottom of the building according to the diagram.

Since the building stands vertically so the triangle made is to be right angled triangle.

Given,

Length of shadow of the building = 31 m

So according to diagram BC = 31 m

The distance from the top of the building to the tip of the shadow = 35

So according to diagram AC = 35 m

We need to find the height of the building i.e. AB according to diagram.

Solution,

Here ΔABC is a right angled triangle, so we apply Pythagoras theorem to find out AB.

" The square of the hypotenuse is equal to the sum of the squares of other two sides".

so we can say that

$AC^2=AB^2+BC^2\\\\AB^2=AC^2-BC^2$

Substituting the values we get;

$AB^2=35^2-31^2= 1225 - 961= 264$

Now taking square root on both side we get;

$\sqrt{AB^2} =\sqrt{264}\\ \\AB = 16.25\ m$

Hence Height of the building is 16.25 meters.