Question 482077: the area of an isosceles triangle is 36m aquared. the equal side is 30 degrees. determine the sum of the sides of the triangle.
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! You have a 30 30 120 degree isosceles trinangle, the first step is to draw the perpeniduclr angle bisector at the 120 degree vertex and turn this into a 30-60-90 triangle.
The formula for the area of the triangle is 1/2bh, the area is given as 36 cm.
The hypotenuse, which is the side of the triangle, and what we are looking for, will be s, the hieght which is in effect the side opposite the 60 in our constructed triangle, will be s / 2.
This comes to 72 = s * s/2.
144 = s^2
83.23 = s^2
x = 9.1 cm, and the side opposite the 60 degree andgle, or the height is 9.1 / 2, which comes out to 7.87.
1/2(9.1)(7.87) = approx 36 as a check.
So what you have now is the size of the side opposite the 30 degree angles, we still need the side opposidte the 120 degree angle.
So, we will use the law of sins, 9.1/ sin 30 = x /sin 120; This worked out to x = 16.28 cm. This is the side opposite the 120 angle.
Two sides of 9.1 plus 16.28 = 34.48 cm for the sum of the sides of the triangle.
Cleomenius.
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