Question

Find the missing side or angle.

Round to the nearest tenth.

b=3

a=9

c=11

C=[ ? ]°

Answer 1

`C=125.0^\circ`

Explanation:

In a triangle:

b=3 ; a=9 ; c=11

We want to determine the value of Angle C.

Since we are given three sides of the triangle, we use the Law of Cosines to find any of the angles.

`c^2=a^2+b^2-2ab\cos C\\11^2=9^2+3^2-2(9)(3)\cos C\\11^2-(9^2+3^2)=-2(9)(3)\cos C\\31=-54\cos C\\\cos C=-(31)/(54) \\C=\arccos (-(31)/(54)) \\C=125.0^\circ$ (to the nearest tenth)`