Find Side Lengths of an Isosceles Triangle

[pcandrepair]

Homework Statement

All three sides of an isoceles triangle are given along with its perimeter. Find the length of each side.
A=97.433 B=41.283 C=41.283
Perimeter=24.78in

Homework Equations

p = a+b+c
a²=b²+c² - 2*b*c*cos(A)

The Attempt at a Solution

Would you somehow find the ratios of the side lengths? And then use the ratios and the perimeter to find the sides? I don't even know if this is possible. We definitely never did these kinds of triangles in geometry class. Thanks for any help :)

 

[Hurkyl]

I see you listed the law of cosines in the equations... but forgot the law of sines...

 

[pcandrepair]

Law of sines: c/sin(A) = c/sin(B) = c/sin(C)

Do I have to solve this as a system of equations to solve for the sides? But where does the given perimeter come into play?

 

[HallsofIvy]

You have many equations:
a+ b+ c= 24.78
b= c
$$c^2= a^2+ b^2- 2abcos(41.283)$$
$$b^2= a^2+ c^2- 2accos(41.283)$$
$$a^2= b^2+ c^2- 2bccos(97.433)$$
$$\frac{a}{sin(97.433)}= \frac{b}{sin(41.283)}$$
$$\frac{a}{sin(97.433)}= \frac{c}{sin(41.283)}$$
$$\frac{b}{sin(41.283)}= \frac{c}{sin(41.283)}$$
Of course, these are not all independent.