Question

8 30° a Solve for a and b using special right triangle rules. b =

Answer 1

$\begin{gathered} a=4\sqrt[]{3} \\ b=4 \end{gathered}$

Explanation

Step 1

we have a rigth triangle, hence let

$\begin{gathered} \text{angle}=\text{ 30} \\ \text{hypotenuse}=8 \\ \text{adjacent side=a} \\ \text{opposite side= b} \end{gathered}$

to find a , we need a function that relates adjacent side, angle and hypotenuse

$\cos \emptyset=\frac{adjacent\text{ side}}{\text{hypotenuse}}$

replace.

$\begin{gathered} \cos \emptyset=\frac{adjacent\text{ side}}{\text{hypotenuse}} \\ \cos \text{ 30=}\frac{a}{8} \\ \text{Multiply both sides by 8} \\ 8\cdot\cos \text{ 30=}\frac{a}{8}\cdot8 \\ a=8\cdot\cos \text{ 30} \\ a=8\cdot\frac{\sqrt[]{3}}{2} \\ a=4\sqrt[]{3} \end{gathered}$

Step 2

now, to find b we can use sine function

$\begin{gathered} \sin \emptyset=\frac{opposite\text{ side}}{\text{hypotenuse}} \\ \end{gathered}$

replace.

$\begin{gathered} \sin 30=\frac{b}{8} \\ \text{Multiply both sidese by 8} \\ 8\cdot\sin 30=\frac{b}{8}\cdot8 \\ 8\sin \text{ 30=b} \\ 4=b \end{gathered}$

I hope this helps you