The length of a shadow of a building is 27m. The distance to the top of the building to the tip of the shadow is 35m. Find the height of the building. If necessary, round your answer to the nearest tenth.

states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides. This theorem can be written as an equation relating the lengths of the sides a, b and c

[tex]a^{2}+b^{2}=c^{2}[/tex]

where

a is the length of a side

b is the length of the other side

c is the length of a hypotenuse (the longest side of the right triangle)

in this case, we need to identify each side of the triangle

Step 1

Let

The length of a shadow of a building is 27m, this is (a)

a=27 m

The distance to the top of the building to the tip of the shadow is 35m,this si the hypotenuse of the triangle(c)

the height of the building is the other side (b)

Step 2

we know a and c, we need isolate c from the equation

[tex]a^{2}+b^{2}=c^{2}\\c^{2}-a^{2}=b^{2}\\b=\sqrt{c^{2}-a^{2}}[/tex]

we are searching for a length, so we only will use the positive root

Step 3

put the values into the equation

[tex]b=\sqrt{c^{2}-a^{2}}\\b=\sqrt{35^{2}-27^{2}}\\b=\sqrt{1225-729}\\ b=\sqrt{496}\\b=22.27 \\[/tex]

so, the height of the building is 22.27 m ≈22 m

I really hope it helps, have a very nice day.