Question

unit exam - right triangles and trigonometry
find the length of side c.
a = 63
b = 61
142°
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

$c^2 = 63^2 + 61^2 - 2(63)(61)\cos(142^\circ)$

Step2: Calculate squared terms

$63^2 = 3969$, $61^2 = 3721$
$c^2 = 3969 + 3721 - 2(63)(61)\cos(142^\circ)$

Step3: Compute product and cosine term

$2(63)(61)=7686$, $\cos(142^\circ)\approx-0.7880$
$c^2 = 7690 - 7686(-0.7880)$

Step4: Simplify the expression

$c^2 = 7690 + 6056.568 = 13746.568$

Step5: Take square root

$c = \sqrt{13746.568}$

Answer:

$117.25$