Question

What are the correct answer for x and y using the options below

Answer 1

ANSWER and EXPLANATION

We have the right angled triangle with one given side and one given angle.

To find x and y, we have to use trigonometric functions SOHCAHTOA.

We have that

`\sin 30\text{ = }(opposite)/(hypotenuse)\text{ and cos30 = }\frac{adjacent\text{ }}{hypotenuse}`

Therefore:

`\begin{gathered} \sin 30\text{ = }(3)/(x) \\ \Rightarrow\text{ x = }(3)/(\sin 30) \\ x\text{ = }(3)/(0.5) \\ x\text{ = 6} \end{gathered}`
`\begin{gathered} \cos 30\text{ = }(y)/(x)\text{ = }(y)/(6) \\ y\text{ = 6cos30} \\ y\text{ = }6\cdot\text{ }\frac{\sqrt[]{3}}{2} \\ y\text{ = 3 }\sqrt[]{3} \end{gathered}`

Those are the values of x and y.

Note: The values of sin30 and cos30 are their standard values.