Question

unit exam - right triangles and trigonometry
find the length of side c.
a = 7
b = 8
∠c = 32°
c =?
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 formula

Substitute $a=7$, $b=8$, $C=32^\circ$ into the Law of Cosines:
$c^2 = 7^2 + 8^2 - 2 \cdot 7 \cdot 8 \cdot \cos(32^\circ)$

Step2: Calculate squared terms and product

Calculate each component:
$7^2=49$, $8^2=64$, $2 \cdot 7 \cdot 8=112$
$c^2 = 49 + 64 - 112 \cdot \cos(32^\circ)$

Step3: Compute sum and cosine value

Sum constants, use $\cos(32^\circ)\approx0.8480$:
$c^2 = 113 - 112 \cdot 0.8480$
$c^2 = 113 - 94.976$

Step4: Solve for c and round

Find $c$ by taking square root:
$c^2 = 18.024$
$c = \sqrt{18.024} \approx 4.25$

Answer:

$4.25$