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 $\angle L$

The sum of angles in a triangle is $180^{\circ}$. 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 the sine - rule to find side $k$

The sine - rule states that $\frac{j}{\sin J}=\frac{k}{\sin K}$. We know $j = 7.2$ km, $\sin J=\sin90^{\circ}=1$, and $\sin K=\sin62^{\circ}\approx0.8829$. So $k=\frac{j\sin K}{\sin J}=\frac{7.2\times\sin62^{\circ}}{\sin90^{\circ}}\approx7.2\times0.8829 = 6.36$ km.

Step3: Use the sine - rule to find side $l$

Using the sine - rule $\frac{j}{\sin J}=\frac{l}{\sin L}$. We know $\sin L=\sin28^{\circ}\approx0.4695$, $\sin J = 1$ and $j = 7.2$ km. So $l=\frac{j\sin L}{\sin J}=\frac{7.2\times\sin28^{\circ}}{\sin90^{\circ}}\approx7.2\times0.4695=3.38$ km.

Answer:

$\angle L = 28^{\circ}$, $k\approx6.36$ km, $l\approx3.38$ km. (Sketch: Draw a right - triangle $\triangle JKL$ with $\angle J = 90^{\circ}$, label $\angle K = 62^{\circ}$, $\angle L=28^{\circ}$, side $j = 7.2$ km, side $k\approx6.36$ km and side $l\approx3.38$ km)