Given, the front of a house is in the shape of an equilateral triangle.
The side of the triangle is 10m.
For equilateral triangle all the three sides are same.
When we find the height of the house, the height is measured from one vertex to the middle of the opposite side. So it will create a right angled triangle.
Let, the right angled triangle here be ABC, where BC is the height of the triangle.
Let, BC = h.
AB is one side of the equilateral triangle = 10m.
AC is half of one side of the equilateral triangle = [tex] (\frac{10}{2} ) [/tex]m = 5m.
Now by using Pythagoras theorem, we know that,
[tex] (AC)^2 +(BC)^2 = (AB)^2 [/tex]
By plugging in the values of AB, AC and BC we will get,
[tex] (5)^2+(h)^2 = (10)^2 [/tex]
[tex] 25+h^2 = 100 [/tex]
To find h^2 now we have to move 25 to the other side by subtracting it from both sides.
[tex] 25+h^2-25 = 100-25 [/tex]
[tex] h^2 = 100-25 [/tex]
[tex] h^2 = 75 [/tex]
To find h, we have to take square root to both sides. By taking square root we will get,
[tex] \sqrt{h^2} = \sqrt{75} [/tex]
[tex] h = 8.7 [/tex] (Approximately taken up to one decimal place)
So the height of the house is 8.7m.
