A triangle has a base of 8 inches and sides of 6 and 5 inches.

Question

What is the height of the triangle?

Round to the nearest hundredth.

 

The height is approximately __?__ in.

Answer 1

Heron's Formula says that if the sides of a triangle are a, b, and c then we define the "semi-perimeter" (s) as:

s = (a + b + c)/2

Then we can say the Area of a triangle = √(s(s - a)(s - b)(s - c))

In this case s = (8 + 6 + 5)/2 = 19/2 = 9.5

So A = √(9.5(9.5 - 8)(9.5 - 6)(9.5 - 5)) = √224.4375 = 14.98123827

We can also say A = 1/2bh so:

14.98123827 = 1/2(8)h

h = 14.98123827/4 = 3.75 in