SOLUTION: finding the value of x in a triangle when you already know the area, q. angle: 53 side length ( hypotenuse) 7.2 base length is x (adjacent) area: 19.6cm2 i need working

Algebra ->  Triangles -> SOLUTION: finding the value of x in a triangle when you already know the area, q. angle: 53 side length ( hypotenuse) 7.2 base length is x (adjacent) area: 19.6cm2 i need working       Log On


   

Question 715008: finding the value of x in a triangle when you already know the area,
q. angle: 53
side length ( hypotenuse) 7.2
base length is x (adjacent)
area: 19.6cm2
i need working out to learn how to do the rest please, thanks
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
As long as you have a hypotenuse, then you know your triangle has a right angle and the side lengths are related using pythagorean theorem identity. Trouble is that you are not given the lengths of either leg.

There are two ways to represent the triangle in this problem. I'll give an example picking the 53 degrees near the top, x base on the bottom, the hypotenuse slanted direction toward the right. The height from the vertex of the 53 degee angle to the vertex of the right angle at the bottom will be 7.2%2Acos%2853%29. A drawing would help to see this.

You are given the area and as a formula this area is (1/2)xh, where h is the height which I described. Since area is 19.6, we can write
%281%2F2%29x%287.2%2Acos%2853%29%29=19.6
and then
highlight%28x=19.6%2A2%2F%287.2%2Acos%2853%29%29%29