Question

Find x.Explain how to find x using trigonometryExplain how to find y using special right triangles.

Answer 1

Step 1: Write out the formula and the special triangle

$\sin \theta=\frac{opp}{hyp}$$\begin{gathered} \text{Where} \\ \theta=\text{ an acute angle in a right-angled triangle} \\ \text{opp = the length of the side of the right-angled triangle opposite but not adjacent to }\theta \\ \text{hyp = the length of the hypotenuse of the right-angled triangle} \end{gathered}$

Step 2 (a): Write out the given values and substitute them into the formula

$\theta=30^0,hyp=24,opp=x$

Therefore,

$\begin{gathered} \sin 30^0=\frac{x}{24} \\ \text{this implies that} \\ \frac{1}{2}=\frac{x}{24} \\ \text{ Cross-multiplying, we have} \\ 2x=24 \\ \text{ Dividing both sides by 2, we have} \\ \frac{2x}{2}=\frac{24}{2} \\ x=12 \end{gathered}$

Step 2(b) Note that for the special triangle in Figure 1

The adjacent of angle 30 degrees is equal √3(the opposite of angle 30 degrees)

Therefore,

$y=\sqrt[]{3}x$