Answer:
[tex]\angle B=43\textdegree\\\\a=21.9\\\\b=20.5[/tex]
Step-by-step explanation:
-This is a Pythagorean Theorem problem.
-A right triangle angle has to complimentary acute angles whose sum add up to 90°:
[tex]\angle B+47\textdegree=90\textdegree\\\\\angle B=43\textdegree[/tex]
-We apply the Sine Rule to solve for a and b:
[tex]\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{c}{Sin \ C}\\\\\\\frac{30}{Sin \ 90}=\frac{b}{Sin \ 43}, sin 90\textdegree=1\\\\\\b=30Sin \ 43\textdegree\\\\=20.5 \ \\\\\# a\\\\\frac{30}{Sin \ 90\textdegree}=\frac{a}{Sin \ 47\textdegree}, Sin \ 90\textdegree=1\\\\a=30Sin \ 47\textdegree\\\\=21.9[/tex]
Hence, a=21.9, b=20.5 and angle B=43°
