Explanation:
We apply sine rule to find the missing sides in each of the triangle.
Reason: Angles and one side are given
a/sin A = c/sinC
a = 4, A = 90°
c = ?, C = 45°
[tex]\begin{gathered} \frac{4}{\sin90\degree}=\frac{c}{\sin45\degree} \\ \text{cross multiply:} \\ 4(\sin \text{ 45) = c (sin 90)} \\ \end{gathered}[/tex][tex]\begin{gathered} In\text{ radical form: sin45 = }\frac{1}{\sqrt[]{2}}=\text{ }\frac{\sqrt[]{2}}{2} \\ 4(\frac{\sqrt[]{2}}{2})\text{ = c(}1) \\ 2\sqrt[]{2}\text{= c} \\ c\text{ = 2}\sqrt[]{2} \end{gathered}[/tex]
a/sinA = h/sinH
a = 2, A = 30°
h = ?, H = 60°
[tex]\begin{gathered} \frac{2}{\sin30}=\frac{h}{\sin60} \\ In\text{ radical form:} \\ \sin \text{ 30 = 1/2, sin }60=\text{ }\frac{\sqrt[]{3}}{2} \\ \frac{2}{\frac{1}{2}}=\frac{h}{\frac{\sqrt[]{3}}{2}} \\ \end{gathered}[/tex][tex]\begin{gathered} 2\times\frac{2}{1}=h\times\frac{2}{\sqrt[]{3}} \\ 4\text{ = }\frac{\text{2h}}{\sqrt[]{3}} \\ 4\sqrt[]{3}\text{ = 2h} \\ \frac{4\sqrt[]{3}}{2}=\frac{2h}{2} \\ h\text{ = }2\sqrt[]{3} \end{gathered}[/tex]
