The front of a house is in the shape of an equilateral triangle with the measure of one side is 10m. Find the height of the house.​

The triangle is 10m on each side.

Set x = height.

Using Pythagorean theoremx^2 + (5 which is is 1/2 of the base)^2

= 10^2 x^2 + 5^2

= 10^2x^2 + 25

= 100subtract 25 from each sidex^2

= 75x

= sqrt(75)

= 8.66m.