in triangle ABC, a = 2, b = the square root of 3, and m,angle C = 30 degrees. What is the value of c?

Question

a= 1 b= 2 c= 2square root of 3 d=square root of 3 over 3

Answer 1

For your first one,
You should recognize those numbers as belonging to the 30-60-90° right-angled triangle
which would make c = 1

If you didn't notice that, you could use the cosine law
c^2 = 2^2 + √3^2 - 2(2)(√)cos30°
= 4 + 3 - 4(√3)(√3/2)
= 7 - 6
c^2 = 1
c = 1

Now, of course , in a triangle with sides, 1 , √3, and 2
2^2 = 1^2 + √3^2
so the triangle is right-angled, etc