Question

Given ABC, mzA = 50°, mzB = 60°, and a = 7. Find c.

Answer 1

7.01.

Explanation:

We can use the Law of Cosines to solve for c:

c^2 = a^2 + b^2 - 2ab*cos(C)

We are given a = 7, m∠A = 50°, and m∠B = 60°. We can use the fact that the angles in a triangle add up to 180° to find m∠C:

m∠C = 180° - m∠A - m∠B

m∠C = 180° - 50° - 60°

m∠C = 70°

Now we can substitute the known values into the Law of Cosines and solve for c:

c^2 = 7^2 + b^2 - 27bcos(70°)

c^2 = 49 + b^2 - 14bcos(70°)

We don't know b, but we can solve for it using the given equation:

3/2 + b = 7/4

Subtracting 3/2 from both sides:

b = 7/4 - 3/2

b = 1/4

Now we can substitute b = 1/4 into the equation for c^2:

c^2 = 49 + (1/4)^2 - 14*(7/4)*(1/4)*cos(70°)

c^2 = 49.1709

c ≈ 7.01

Therefore, the length of side c is approximately 7.01.