Question

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Answer 1

`AB = 8.38`

Explanation:

Given

`AC = 9`

`BC =10`

`\angle B = 52`

Required

Determine AB

This question will be answered using the cosine law.

`(AB)^2 = (AC)^2 + (BC)^2 - 2(AC)(BC)\ \cos \angle B`

Substitute the expected values

`(AB)^2 = 9^2 + 10^2 - 2 * 9 * 10 * cos(52)`

`(AB)^2 = 81 + 100 - 180* cos(52)`

`(AB)^2 = 181 - 180* cos(52)`

`(AB)^2 = 181 - 180* 0.6157`

`(AB)^2 = 70.174`

Take square roots of both sides

`AB = \sqrt{70.174`

`AB = 8.38` -- approximated