the length of the base of an isosceles triangle is 5507meter

the length of the base of an isosceles triangle is 55.07meters. Each base angle is 31.89°.Find the length of each of the two equal sides of the triangle.

Solution

Each base angle is 31.89°

==>let third angle be x

x+31.89+31.89=180

x =180-(2*31.89)

x=116.22⁰

let the length of 2 equal sides by a

by law of cosines

55.07²=a²+a² -2*a*a*cos(116.22)

55.07²=2a² -2a²cos(116.22)

55.07²=2a²(1-cos(116.22))

a²=55.07²/(2(1-cos(116.22)))

a=[55.07²/(2(1-cos(116.22)))]^1/2

a=32.43

length of each of the two equal sides of the triangle.=32.43 meters