Question

Solve the triangle
a
b
c
d

Answer 1

B

Explanation:

Use the Law of Cosines to find the measure of segment c:

`c=√(a^2+b^2-2ab*cos(C))\\\\c=√(12^2+13^2-2(12)(13)*cos(134))\\\\c=√(313-312cos(134))\\\\c=√(313-312(-.6946583705))\\\\c=√(313-(-216.7334116))\\\\c=√(313+216.7334116)\\\\c=√(529.7334116)\\`

c ≈ 23.01593821 km ≈ 23 km

Since c = 23 km, our only options are choices B and D. Now, let's find the measure of angle A to confirm. To do this we will use the Law of Sines:

`(sin(A))/(a) =(sin(C))/(c) \\\\(sin(A))/(12)=(sin(134))/(23.01593821)\\\\sin(A)=12((sin(134))/(23.01593821))\\\\A=sin^(-1)[12((sin(134))/(23.01593821))]\\\\`

A ≈ 22.02726885° ≈ 22°

Since the measure of c = 23 km and the measure of angle A = 22°, the answer must be choice B.