2 Answers

Vasiliykarasev · Answer 1 · 2021-01-31T05:21:04+0000

We have been given that in ΔJKL, k = 22 cm, ∠L=23° and ∠J=26°. We are asked to find the length of j to the nearest tenth of a centimeter.

We will use law of sines to solve for side j.

$\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}$ , where, a, b and c are opposite sides to angles A, B and C respectively.

We need to find measure of angle K to apply law of sine to our given problem.

Using angle sum property, we will get:

$\angle J+\angle K+\angle L=180^(\circ)$

$26^(\circ)+\angle K+23^(\circ)=180^(\circ)$

$\angle K+49^(\circ)=180^(\circ)$

$\angle K+49^(\circ)-49^(\circ)=180^(\circ)-49^(\circ)$

$\angle K=131^(\circ)$

$\frac{j}{\text{sin}(J)}=\frac{k}{\text{sin}(K)}$

$\frac{j}{\text{sin}(26^(\circ))}=\frac{22}{\text{sin}(131^(\circ))}$

$\frac{j}{\text{sin}(26^(\circ))}\cdot \text{sin}(26^(\circ))=\frac{22}{\text{sin}(131^(\circ))}\cdot \text{sin}(26^(\circ))$

$j=(22)/(0.754709580223)\cdot 0.438371146789$

j=(9.644165229358)/(0.754709580223)

j=12.77864423889

Upon rounding to nearest tenth, we will get:

$j\approx 12.8$

Therefore, the length of j is approximately 12.8 cm.

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