given the image, find ( mangle k ). if necessary, round to the nearest tenth. ( 20.5^{circ} ) ( 22.0^{circ} ) ( 68.0^{circ} ) ( 69.5^{circ} )

Question

Accepted Answer

# Answer:
$22.0^{\circ}$

# Explanation:
## Step1: Recall the cosine function
In a right - triangle $\triangle KLM$ with $\angle L = 90^{\circ}$, the cosine of an angle $\theta$ is defined as $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle K$, the adjacent side to $\angle K$ is $KL = 6.5$ and the hypotenuse is $KM=\sqrt{301}\approx17.35$.
## Step2: Calculate $\cos\angle K$
$\cos\angle K=\frac{KL}{KM}=\frac{6.5}{\sqrt{301}}$.
## Step3: Find $\angle K$
$\angle K=\cos^{- 1}(\frac{6.5}{\sqrt{301}})$.
$$
\begin{align*}
\frac{6.5}{\sqrt{301}}&\approx\frac{6.5}{17.35}\
\cos^{-1}(0.3746)&\approx22.0^{\circ}
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the cosine function

Step2: Calculate \(\cos\angle K\)

Step3: Find \(\angle K\)

Answer: