In triangle ABC,M<A=39,a=11,and b=13. Find c to the nearest tenth.

Question

A 8.3

B. 9.2

C. 19.8

D. 17.5

Answer 1

Use the law of cosines, which states that for a triangle ABC with sides a, b, and c:

c² = a² + b² - 2abcos(c).

Since we know m∠A, a, and b, let's replace the variables in the formula to work in our favor:

a² = c² + b² - 2cbcos(m∠A)

11² = c² + 13² - 2c(13)cos(39°)

0 = c² - 26cos(39°)c + 48

Use the quadratic formula to get the roots: c ≈ 2.8, 17.5

Therefore, D is our answer!