What is the height of a triangle that has two 100 m long sides and one 120 m long side?
A.
40 meters
B.
60 meters
C.
80 meters
D.
100 meters
E.
110 meters
We can use the formula for the area of a triangle, which is given by:
area = (1/2) * base * height
In this case, the base is the 120 m long side and we need to find the height. To do this, we can rearrange the formula as:
height = (2 * area) / base
We can also use Heron's formula to find the area of the triangle:
s = (100 + 100 + 120) / 2 = 160
area = sqrt(s * (s - 100) * (s - 100) * (s - 120)) = 4000
Substituting these values into the formula for the height, we get:
height = (2 * 4000) / 120 = 66.67
Rounding to the nearest tenth, the height is approximately 66.7 m. Therefore, the closest answer choice is B. 60 meters.