Question

In △ABC, m∠A=52
°, c=11
, and m∠B=19
°. Find a
to the nearest tenth

Answer 1

9.2

Explanation:

Well since you're given two angles you can find the other angle by subtracting the sum of those two known angles from 180

so m<C = 180 - (52 + 19) = 109

m<C = 109

So know that you have the angle C and the side c, as well as the angle A you can use this information to solve for side a using the law of sines.

The law of sines states that:
`(a)/(sin A) = (c)/(sin C)` which works for any two sides and angles of the triangle.

So now we can plug the known information in to solve for side a

`(a)/(sin 52) = (11)/(sin 109)\\\\a=(11)/(sin109)*sin52\\a\approx11.634 * 0.788\\a\approx9.168\\a\approx9.2`