find w.

write your answer as an integer or as a decimal rounded to the nearest ten

Question

find w.

write your answer as an integer or as a decimal rounded to the nearest ten

Accepted Answer

# Explanation:
## Step1: Find the third angle
The sum of angles in a triangle is $180^{\circ}$. Let the third angle be $m\angle X$.
$m\angle X=180^{\circ}-(115^{\circ}+13^{\circ}) = 52^{\circ}$
## Step2: Apply the Law of Sines
The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$.
In $\triangle VWX$, we have $\frac{w}{\sin13^{\circ}}=\frac{8}{\sin52^{\circ}}$
## Step3: Solve for $w$
$$
\begin{align*}
w&=\frac{8\times\sin13^{\circ}}{\sin52^{\circ}}\
\sin13^{\circ}&\approx0.2225,\sin52^{\circ}\approx0.7880\
w&=\frac{8\times0.2225}{0.7880}\
w&=\frac{1.78}{0.7880}\
w&\approx2.3
\end{align*}
$$

# Answer:
$2.3$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find the third angle

Step2: Apply the Law of Sines

Step3: Solve for \(w\)

Answer: