Question

find the length of the indicated side.
30
141°
32
?
round to the nearest tenth

Explanation:

Step1: Apply the Law of Cosines

Let the unknown side be $c$, the two known sides be $a=30$, $b=32$, and the included angle $C=141^\circ$. The Law of Cosines formula is:
$$c^2 = a^2 + b^2 - 2ab\cos(C)$$

Step2: Substitute known values

$$c^2 = 30^2 + 32^2 - 2(30)(32)\cos(141^\circ)$$
Calculate each term:
$30^2=900$, $32^2=1024$, $\cos(141^\circ)\approx-0.7771$
$$c^2 = 900 + 1024 - 2(30)(32)(-0.7771)$$

Step3: Compute the expression

$$c^2 = 1924 + 1501.632$$
$$c^2 = 3425.632$$

Step4: Solve for $c$

$$c = \sqrt{3425.632}$$
$$c\approx58.5$$

Answer:

58.5