Answer:
[tex]AB = 8.38[/tex]
Step-by-step explanation:
Given
[tex]AC = 9[/tex]
[tex]BC =10[/tex]
[tex]\angle B = 52[/tex]
Required
Determine AB
This question will be answered using the cosine law.
[tex](AB)^2 = (AC)^2 + (BC)^2 - 2(AC)(BC)\ \cos \angle B[/tex]
Substitute the expected values
[tex](AB)^2 = 9^2 + 10^2 - 2 * 9 * 10 * cos(52)[/tex]
[tex](AB)^2 = 81 + 100 - 180* cos(52)[/tex]
[tex](AB)^2 = 181 - 180* cos(52)[/tex]
[tex](AB)^2 = 181 - 180* 0.6157[/tex]
[tex](AB)^2 = 70.174[/tex]
Take square roots of both sides
[tex]AB = \sqrt{70.174[/tex]
[tex]AB = 8.38[/tex] -- approximated
