Question

i need help with this question... it's about special right triangles. The answer should not be a decimal.

Answer 1

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,

`\begin{gathered} \cos 30\text{ = }\frac{\sqrt[]{3}}{2} \\ \text{Thus, } \\ \frac{\sqrt[]{3}}{2}\text{ =}(x)/(34) \\ 2x=34\sqrt[]{3} \\ x\text{ = }\frac{34\sqrt[]{3}}{2} \\ x\text{ = 17}\sqrt[]{3} \end{gathered}`

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