Question

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

Answer 1

we are given a right triangle with one side and one angle known, we are asked to find the other two sides. We can make use of trigonometric functions to find one of the sides. We will use tangent to find side "x", since this function relates the opposite and adjacent sides of the triangle. The function would be like this:

`\tan 60=\frac{10\sqrt[]{3}}{x}`

Solving fo "x", we get:

`x=\frac{10\sqrt[]{3}}{\tan 60}`

Now, the exact value of "tan 60" is the following:

`\tan 60=\sqrt[]{3}`

Replacing that in the equation for "x", we get:

`x=\frac{10\sqrt[]{3}}{\sqrt[]{3}}=10`

Therefore, x = 10.

To find the value of "y" we can use the Pythagorean theorem, which relates the hypotenuse with the other two sides, like this:

`y^2=(10)^2+(10\sqrt[]{3})^2`

solving the operations we get:

`\begin{gathered} y^2=100+100(3) \\ y^2=100+300 \\ y^2=400 \end{gathered}`

Taking square root on both sides, we get:

`y=\sqrt[]{400}=20`

Therefore, y = 20