Question

find the measure of angle c.
c = ?°
law of cosines: c² = a² + b² - 2ab·cosc
round your final answer to the nearest tenth.

Explanation:

Step1: Substitute values into the Law of Cosines formula

Given \(a = 55\), \(b = 90\), \(c = 50\), and the formula \(c^{2}=a^{2}+b^{2}-2ab\cos C\).
Substitute: \(50^{2}=55^{2}+90^{2}-2\times55\times90\times\cos C\).
Calculate squares: \(2500 = 3025+8100 - 9900\cos C\).

Step2: Simplify the equation

First, add \(3025\) and \(8100\): \(2500=11125 - 9900\cos C\).
Then, rearrange for \(\cos C\): \(9900\cos C=11125 - 2500\).
\(9900\cos C = 8625\).
So, \(\cos C=\frac{8625}{9900}\).

Step3: Calculate the angle \(C\)

\(C=\cos^{-1}(\frac{8625}{9900})\).
Using a calculator, \(C\approx29.5^{\circ}\).

Answer:

\(29.5\)