multiple choice 1 point
in △jkl, j = 7 cm, k = 6 cm, and m∠l = 35°. find m∠j.
22°
58°
19°
87°

Question

Accepted Answer

# Explanation:
## Step1: Use the Law of Cosines
First, find the length of side $l$ using the Law of Cosines: $l^{2}=j^{2}+k^{2}-2jk\cos L$.
Substitute $j = 7$, $k = 6$, and $L=35^{\circ}$:
$$
\begin{align*}
l^{2}&=7^{2}+6^{2}-2\times7\times6\times\cos35^{\circ}\
l^{2}&=49 + 36-84\times0.8192\
l^{2}&=85-68.8128\
l^{2}&=16.1872\
l&\approx4.02
\end{align*}
$$
## Step2: Use the Law of Sines
Then, use the Law of Sines $\frac{\sin J}{j}=\frac{\sin L}{l}$.
Substitute $j = 7$, $l\approx4.02$, and $L = 35^{\circ}$:
$$
\begin{align*}
\sin J&=\frac{j\sin L}{l}\
\sin J&=\frac{7\times\sin35^{\circ}}{4.02}\
\sin J&=\frac{7\times0.5736}{4.02}\
\sin J&=\frac{4.0152}{4.02}\
\sin J&\approx0.999
\end{align*}
$$
Since $\sin J\approx0.999$, $J\approx87^{\circ}$

# Answer:
$87^{\circ}$ (the fourth option)

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QUESTION IMAGE

Question

Explanation:

Step1: Use the Law of Cosines

Step2: Use the Law of Sines

Answer: