Question

Find the values of x and y. Express your answers in simplest radical form.

Answer 1

this is a 30-60-90 special right triangle,
x=half of the hypotenuse=1/2 of 24=12
y=(√3)/2 of the hypotenuse=12√3

Answer 2

`x=12`

`y=12√(3)`

Explanation:

We have been given diagram of a triangle. We are asked to find the values of x and y for the given triangle.

We will use law of trigonometric ratios to find the sides of our given triangle.

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{sin}(60^(\circ))=(y)/(24)`

`(√(3))/(2)=(y)/(24)`

`(√(3))/(2)\cdot 24=(y)/(24)\cdot 24`

`(√(3))/(1)\cdot 12=y`

`y=12√(3)`

Therefore, the value of y is
`12√(3)`.

`\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}`

`\text{cos}(60^(\circ))=(x)/(24)`

`(1)/(2)=(x)/(24)`

`(1)/(2)}\cdot 24=(x)/(24)\cdot 24`

`x=12`

Therefore, the value of x is 12.