Question

Find the value of the variable. If you’re answer is not an intervene leave it in simplest radical form.

Answer 1

Find the value of x and y in the right angled triangle;

`\begin{gathered} \text{Opposite}=y\text{ (facing the reference angle)} \\ \text{Adjacent}=x\text{ (lies between the reference angle and the right angle)} \\ \text{Hypotenuse}=16\sqrt[]{3}\text{ (facing the right angle)} \end{gathered}`

To calculate x, we shall use the trig ratio;

`\begin{gathered} \cos \theta=(adj)/(hyp) \\ \cos 30=\frac{x}{16\sqrt[]{3}} \\ \text{Note that cos 30 is also equal to }\frac{\sqrt[]{3}}{2}.\text{ Therefore} \\ \frac{\sqrt[]{3}}{2}=\frac{x}{16\sqrt[]{3}} \\ \text{Cross multiply and you'll have} \\ \frac{16\sqrt[]{3}*\sqrt[]{3}}{2}=x \\ (16*3)/(2)=x \\ x=24 \end{gathered}`

To valculate y, we shall use the trig ratio;

`\begin{gathered} \sin \theta=(opp)/(hyp) \\ \sin 30=\frac{y}{16\sqrt[]{3}} \\ Note\text{ that sin 30 is also equal to }(1)/(2).\text{ Therefore} \\ (1)/(2)=\frac{y}{16\sqrt[]{3}} \\ \text{Cross multiply and you'll have} \\ \frac{16\sqrt[]{3}}{2}=y \\ y=8\sqrt[]{3} \end{gathered}`

The first option is the correct answer

x = 24, y = 8 square root 3