Question

In ALJK, k = 480 cm, j = 420 cm and LJ=43°. Find all possible values of ZK, to the

Answer 1

Answer:

$K \approx 51.2^\circ$

$K \approx 128.8^\circ$

Step-by-step explanation:

Given

$k = 480$

$j = 420$

$\angle J = 43^\circ$

Required

Find the measure of K

The value of K ranges from: $0^\circ \le K \le 180^\circ$

To do this, we apply sine rule;

$\frac{j}{\sin J} = \frac{k}{\sin K}$

So, we have:

$\frac{420}{\sin 43} = \frac{480}{\sin K}$

Cross multiply

$\sin K * 420 = \sin 43 * 480$

Make sin K the subject

$\sin K= \frac{\sin 43 * 480}{420}$

$\sin K= \frac{0.6820 * 480}{420}$

$\sin K= 0.7794$

Take arc sin of both sides

$K = sin^{-1}(0.7794)$

$K \approx 51.2^\circ$

Recall that: $0^\circ \le K \le 180^\circ$

The other possible value of K is:

$K \approx 180 - 51.2$

$K \approx 128.8^\circ$