Question

find the measure of angle c.
c
b
a
c
c = 20
a = 11
b = 12
c = ？°

Explanation:

Step1: Use the Law of Cosines

The Law of Cosines formula is \(c^{2}=a^{2}+b^{2}-2ab\cos C\).
Substitute \(a = 11\), \(b = 12\), and \(c = 20\) into the formula:
\(20^{2}=11^{2}+12^{2}-2\times11\times12\times\cos C\).

Step2: Simplify the equation

Calculate the squares:
\(400 = 121+144-264\cos C\).
\(400=265 - 264\cos C\).

Step3: Solve for \(\cos C\)

Rearrange the equation:
\(264\cos C=265 - 400\).
\(264\cos C=- 135\).
\(\cos C=\frac{-135}{264}\approx - 0.511\).

Step4: Find the angle \(C\)

Take the inverse cosine:
\(C=\cos^{-1}(-0.511)\).
Using a calculator, \(C\approx120.7^{\circ}\).

Answer:

\(120.7^{\circ}\)