Question

Find the value of the variable(s). If youranswer is not an integer, leave it in simplest radical form. 7 11 300 Not drawn to scale

Answer 1

In the given figure

There is a right triangle whose legs are 11, x, and its hypotenuse is y

The side opposite to the angle of measure 30 degrees is 11

The side adjacent to the angle of measure 30 degrees is x

Let us use the trigonometry ratios to find x and y

`\because\sin 30=(opp)/(hyp)`

The opposite is 11 and the hypotenuse is y

`\therefore\sin 30=(11)/(y)`
`\because\sin 30=(1)/(2)`
`\therefore(1)/(2)=(11)/(y)`

By using cross multiplication

`\begin{gathered} \therefore1* y=2*11 \\ \therefore y=22 \end{gathered}`
`\because\cos 30=(adj)/(hyp)`