Question

Can someone help meeee ASAP. For 10 points

Answer 1

Answer:

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

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°:

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

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

$\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{c}{Sin \ C}\\\\\\\frac{30}{Sin \ 90}=\frac{b}{Sin \ 43}, sin 90\textdegree=1\\\\\\b=30Sin \ 43\textdegree\\\\=20.5 \ \\\\\# a\\\\\frac{30}{Sin \ 90\textdegree}=\frac{a}{Sin \ 47\textdegree}, Sin \ 90\textdegree=1\\\\a=30Sin \ 47\textdegree\\\\=21.9$

Hence, a=21.9, b=20.5  and angle B=43°