SOLUTION: If I have a triangle with an area of 80cm^2, and two sides are 19.2 and 11.3, how do I figure out the angle between the two lengths?

Algebra ->  Triangles -> SOLUTION: If I have a triangle with an area of 80cm^2, and two sides are 19.2 and 11.3, how do I figure out the angle between the two lengths?      Log On


   

Question 712094: If I have a triangle with an area of 80cm^2, and two sides are 19.2 and 11.3, how do I figure out the angle between the two lengths?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Guessing an acute angle, taking the longer side as the base, the shorter side multiplied by sine of the angle is the height. Area is (1/2)(b)*h, or how I just described, Area = %281%2F2%29%2819.2%29%2811.3%29sin%28x%29, assuming name of the angle is x.

From highlight%28%281%2F2%29%2819.2%29%2811.3%29sin%28x%29=80%29 obtain sine%28x%29=%282%2A80%29%2F%2819.2%2A11.3%29
sin(x)=0.73745, highlight%28x=47.5%29 degrees.

In this picture below, the two sides of the triangle are shown, and the height is shown; but the third triangle side is not shown.