Question

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

Explanation:

Step1: Identify known values

We know \( a = 29 \), \( b = 50 \), \( c = 26 \), and the Law of Cosines formula \( c^{2}=a^{2}+b^{2}-2ab\cdot\cos(C) \).

Step2: Substitute values into the formula

Substitute \( a = 29 \), \( b = 50 \), \( c = 26 \) into the formula:

$$ 26^{2}=29^{2}+50^{2}-2\times29\times50\times\cos(C) $$

Calculate each term:
\( 26^{2}=676 \), \( 29^{2}=841 \), \( 50^{2}=2500 \)
So the equation becomes:

$$ 676 = 841+2500 - 2900\times\cos(C) $$

Step3: Simplify the equation

First, calculate \( 841 + 2500=3341 \)
Then the equation is:

$$ 676=3341 - 2900\cos(C) $$

Rearrange to solve for \( \cos(C) \):

$$ 2900\cos(C)=3341 - 676 $$

$$ 2900\cos(C)=2665 $$

$$ \cos(C)=\frac{2665}{2900} $$

Simplify \( \frac{2665}{2900}\approx0.919 \)

Step4: Find angle C

Take the inverse cosine (arccos) of \( 0.919 \):

$$ C=\arccos(0.919)\approx23.3^{\circ} $$

Answer:

\( \approx23.3^{\circ} \) (The answer may vary slightly depending on the calculator's precision)