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