what is the length of y?
round to the nearest tenth. y≈type your answer...

Question

Accepted Answer

# Explanation:
## Step1: Apply the Law of Cosines
The Law of Cosines formula is $ y^{2}=x^{2}+z^{2}-2xz\cos Y$. Here, $x = 7$, $z = 10$, and $Y=32^{\circ}$.
$$
\begin{align*}
y^{2}&=7^{2}+10^{2}-2\times7\times10\times\cos(32^{\circ})\
y^{2}&=49 + 100-140\times\cos(32^{\circ})
\end{align*}
$$
## Step2: Calculate $\cos(32^{\circ})$
We know that $\cos(32^{\circ})\approx0.848$.
$$
\begin{align*}
y^{2}&=49+100 - 140\times0.848\
y^{2}&=149-118.72\
y^{2}&=30.28
\end{align*}
$$
## Step3: Solve for $y$
Take the square - root of both sides: $y=\sqrt{30.28}\approx5.5$

# Answer:
$5.5$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Apply the Law of Cosines

Step2: Calculate \(\cos(32^{\circ})\)

Step3: Solve for \(y\)

Answer: