Answer:
Step-by-step explanation:
a. This is a right triangle with two sides and one angle given.
-We apply Sine Rule to find the angle B:
[tex]\frac{a}{Sin \ A}=\frac{b}{Sin \ B}=\frac{b}{Sin \ C}[/tex]
-The sides given are 10and 17 and the right angle 90°
[tex]\frac{17}{Sin \ 90 \textdegree}=\frac{10}{Sin \ m\angle B}\\\\m\angle B=Sin^{-1}\frac{10}{(17/Sin \ 90\textdegree)}\\\\=36.03\textdegree[/tex]
Hence the angle B is 36.03°
b.We again use the sine rule to obtain the unknown angle w:
-15 corresponds to 90° and 9 corresponds to w°
[tex]\frac{a}{Sin \ a}=\frac{b}{Sin \ B}\\\\\frac{15}{Sin \ 90\textdegree}=\frac{9}{Sin \ w\textdegree}\\\\\\\\w=Sin^{-1}(\frac{9}{15}), \ \ Sin \ 90\textdegree=1\\\\=36.87\textdegree[/tex]
Hence, the measure of w is 36.87°
