Question

find the measure of angle c.
c = ?°
b = 50
a = 29
a
c = 26
b
law of cosines: $c^2 = a^2 + b^2 - 2ab \cdot \cos(c)$
round your answer to the nearest hundredth.

Explanation:

Step1: Substitute values into Law of Cosines

We know \(a = 29\), \(b = 50\), \(c = 26\). Substitute into \(c^{2}=a^{2}+b^{2}-2ab\cdot\cos(C)\):
\(26^{2}=29^{2}+50^{2}-2\times29\times50\times\cos(C)\)
Calculate each term: \(26^{2}=676\), \(29^{2}=841\), \(50^{2}=2500\).
So, \(676 = 841 + 2500 - 2900\cos(C)\).

Step2: Simplify the equation

Combine like terms: \(841 + 2500 = 3341\).
Equation becomes: \(676 = 3341 - 2900\cos(C)\).
Rearrange to solve for \(\cos(C)\):
\(2900\cos(C)=3341 - 676\)
\(2900\cos(C)=2665\)
\(\cos(C)=\frac{2665}{2900}\approx0.91897\).

Step3: Find angle \(C\)

Take the inverse cosine: \(C=\cos^{-1}(0.91897)\).
Using a calculator, \(C\approx23.32^{\circ}\) (rounded to nearest hundredth).

Answer:

\(23.32\)