find the value of each variable.\n$x = \\square$ and $y = \\square$\n(simplify your answers. type exact…
find the value of each variable.\n$x = \\square$ and $y = \\square$\n(simplify your answers. type exact answers, using radicals as needed.)
Answer
Explanation:
Step1: Identify triangle type
This is a 30-60-90 right triangle, hypotenuse = 36.
Step2: Solve for x (opposite 30°)
In 30-60-90 triangles, side opposite 30° is $\frac{1}{2}$ hypotenuse. $x = \frac{1}{2} \times 36 = 18$
Step3: Solve for y (adjacent to 30°)
Use Pythagorean theorem: $y = \sqrt{36^2 - x^2}$ $y = \sqrt{1296 - 324} = \sqrt{972} = 18\sqrt{3}$
Answer:
$x = 18$ and $y = 18\sqrt{3}$