What is the height of a triangle that has two 100 m long sides and one 120 m long side?

Answer 1

To find the height of the triangle, we need to use the formula:

Area = 1/2 * base * height

where the base is the 120 m long side and the height is what we're trying to find.

We also know that the area of the triangle can be calculated using Heron's formula:

Area = √(s(s-a)(s-b)(s-c))

where a,b,c are the sides of the triangle and s is the semiperimeter (half the perimeter):

s = (a+b+c)/2

Putting it all together, we get:

Area = 1/2 * 120 * height = √(s(s-a)(s-b)(s-c))

s = (100+100+120)/2 = 160

Area = 1/2 * 120 * height = √(160(160-100)(160-100)(160-120))

Area = 1/2 * 120 * height = √(160*60*60*40)

Area = 1/2 * 120 * height = 14400

Solving for height, we get:

height = (2*14400)/120 = 240

Therefore, the height of the triangle is 240 meters.