Question

1. sketch each triangle and solve if possible. (solve means to find all the missing angles and side lengths). in a diagram in your answer. in △jkl, <j = 90°, <k=62° and j=7.2 km

Explanation:

Step1: Find angle L

The sum of angles in a triangle is 180°. So, $\angle L=180^{\circ}-\angle J - \angle K$. Given $\angle J = 90^{\circ}$ and $\angle K=62^{\circ}$, then $\angle L=180^{\circ}-90^{\circ}-62^{\circ}=28^{\circ}$.

Step2: Use sine - ratio to find side k

We know that $\sin K=\frac{k}{j}$. Given $j = 7.2$ km and $\angle K = 62^{\circ}$, then $k = j\sin K=7.2\times\sin62^{\circ}\approx7.2\times0.8829 = 6.36$ km.

Step3: Use cosine - ratio to find side l

We know that $\cos K=\frac{l}{j}$. Given $j = 7.2$ km and $\angle K = 62^{\circ}$, then $l = j\cos K=7.2\times\cos62^{\circ}\approx7.2\times0.4695 = 3.38$ km.

Answer:

$\angle L = 28^{\circ}$, $k\approx6.36$ km, $l\approx3.38$ km