Answer:
A) y = [tex]\frac{11\sqrt{3} }{2}[/tex], 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
[tex]\sqrt{3}[/tex] = y/(11/2)
Multiplying both sides by 11/2, we get
[tex]\frac{11\sqrt{3} }{2}[/tex] = 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 + ([tex]\frac{11\sqrt{3} }{2}[/tex])² = x²
Simplifying this, we get
[tex]\frac{121}{4}[/tex] + [tex]\frac{121 * 3}{4}[/tex] = 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!
