Question

Can someone help meeee ASAP. For 10 points

Answer 1

`\angle B=43\textdegree\\\\a=21.9\\\\b=20.5`

Explanation:

-This is a Pythagorean Theorem problem.

-A right triangle angle has to complimentary acute angles whose sum add up to 90°:

`\angle B+47\textdegree=90\textdegree\\\\\angle B=43\textdegree`

-We apply the Sine Rule to solve for a and b:

`(a)/(Sin \ A)=(b)/(Sin \ B)=(c)/(Sin \ C)\\\\\\(30)/(Sin \ 90)=(b)/(Sin \ 43), sin 90\textdegree=1\\\\\\b=30Sin \ 43\textdegree\\\\=20.5 \ \\\\\# a\\\\(30)/(Sin \ 90\textdegree)=(a)/(Sin \ 47\textdegree), Sin \ 90\textdegree=1\\\\a=30Sin \ 47\textdegree\\\\=21.9`

Hence, a=21.9, b=20.5 and angle B=43°