Question

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

nearest 10th of a degree.

Answer 1

`K \approx 51.2^\circ`

`K \approx 128.8^\circ`

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;

`(j)/(\sin J) = (k)/(\sin K)`

So, we have:

`(420)/(\sin 43) = (480)/(\sin K)`

Cross multiply

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

Make sin K the subject

`\sin K= (\sin 43 * 480)/(420)`

`\sin K= (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`