Question

Question
Find the missing side lengths. Leave answer in simplest
radical form.

Answer 1

A) y =
`(11√(3) )/(2)`, x = 11

Explanation:

We can use the 60 degree angle to help us solve this.

Remember: tan(angle) = opposite/adjacent

Using this formula, we get that

tan (60 degrees) = y / (11/2)

This is because y is the side opposite to the 60 degree angle and 11/2 is the side adjacent to the 60 degree angle.

Simplifying this expression, we get that

`√(3)` = y/(11/2)

Multiplying both sides by 11/2, we get

`(11√(3) )/(2)` = y

We can now use the pythagorean theorem to help us solve for x

Remember: a² + b² = c²

Since x is the hypotenuse, it is the c value. Therefore, we get:

(11/2)² + (
`(11√(3) )/(2)`)² = x²

Simplifying this, we get

`(121)/(4)` +
`(121 * 3)/(4)` = x²

Simplifying this some more, we get

484/4 = x²

121 = x²

Taking the square root of both sides, we get that

x = 11

I hope this helps!