Question

solve for c. evaluate and simplify c² = 3² + 10² - 2(3)(10)cos(34°) c = ? enter the value of c. round to the nearest tenth.

Explanation:

Step1: Calculate the squares and products

First, calculate $3^{2}=9$, $10^{2} = 100$, and $2\times3\times10=60$.
The equation $c^{2}=3^{2}+10^{2}-2(3)(10)\cos(34^{\circ})$ becomes $c^{2}=9 + 100-60\cos(34^{\circ})$.

Step2: Find the value of $\cos(34^{\circ})$

We know that $\cos(34^{\circ})\approx0.829$.
Then $60\cos(34^{\circ})\approx60\times0.829 = 49.74$.

Step3: Calculate the value of $c^{2}$

$c^{2}=9 + 100-49.74=109 - 49.74 = 59.26$.

Step4: Solve for $c$

$c=\sqrt{59.26}\approx7.7$.

Answer:

$7.7$