Question

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

Answer 1

Answer:

A) y = $\frac{11\sqrt{3} }{2}$, x = 11

Step-by-step 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

$\sqrt{3}$ = y/(11/2)

Multiplying both sides by 11/2, we get

$\frac{11\sqrt{3} }{2}$ = 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 + ($\frac{11\sqrt{3} }{2}$)² = x²

Simplifying this, we get

$\frac{121}{4}$ + $\frac{121 * 3}{4}$ = 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!