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 \( 841+2500 = 3341 \)
The equation is now:

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

Subtract 3341 from both sides:

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

\( 676-3341=-2665 \)
So:

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

Step4: Solve for \( \cos(C) \)

Divide both sides by - 2900:

$$ \cos(C)=\frac{-2665}{-2900}=\frac{2665}{2900}\approx0.919 $$

Step5: Find the angle \( C \)

Take the inverse cosine (arccos) of 0.919:

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

Answer:

\( 23.3 \) (rounded to one decimal place, the value may vary slightly depending on the calculator's precision)