4) The given triangle is a right angle triangle. Taking 30 degrees as the reference angle,
hypotenuse = 34
adjacent side = x
opposite side = y
We would find x by applying the Cosine trigonometric ratio which is expressed as
Cos# = adjacent side/hypotenuse
Cos 30 = x/34
Recall,
[tex]\begin{gathered} \cos 30\text{ = }\frac{\sqrt[]{3}}{2} \\ \text{Thus, } \\ \frac{\sqrt[]{3}}{2}\text{ =}\frac{x}{34} \\ 2x=34\sqrt[]{3} \\ x\text{ = }\frac{34\sqrt[]{3}}{2} \\ x\text{ = 17}\sqrt[]{3} \end{gathered}[/tex]
To find y, we would apply the Sine trigonometric ratio. It is expressed as
Sin# = opposite side/hypotenuse
Sin30 y/34
Recall, Sin30 = 0.5. Thus
0.5 = y/34
y = 0.5 * 34
y = 17
