Question

May I please get get help with this. For I am confused as I have tried multiple times to get the correct answers for it

Answer 1

`\begin{gathered} c\text{ = }\frac{3\text{ }\sqrt[]{2}}{2} \\ a\text{ = 10} \end{gathered}`Step-by-step explanation:

For the smaller triangle:

angle = 45°

opposite = c

hypotenuse = 3

To get c, we will apply sine rule:

`\begin{gathered} \sin \text{ 45}\degree\text{ = }\frac{opposite}{\text{hypotenuse}} \\ \sin \text{ 45}\degree\text{ = }(c)/(3) \\ c\text{ = 3(sin45}\degree)\text{ = 3(}\frac{\sqrt[]{2}}{2}) \\ c\text{ = }\frac{3\text{ }\sqrt[]{2}}{2} \end{gathered}`

For the larger triangle:

angle = 30°

opposite = 5

hypotenuse = a

To get a, we will apply sine rule:

`\begin{gathered} \sin \text{ 30}\degree\text{ = }(opposite)/(hypotenuse) \\ \sin \text{ 30}\degree\text{ = }(5)/(a) \\ \text{cross multiply:} \\ a\text{ (sin 30}\degree)\text{ = 5} \\ a\text{ = }\frac{5}{\text{sin 30}\degree\text{ }} \\ a\text{ = }(5)/((1)/(2))\text{ = 5 }*(2)/(1) \\ a\text{ = 10} \end{gathered}`