Answer:
x = 16√3
y = 8√3
Explanation:
First, to figure out x, put the side we already know (24) over the cosine of the angle we know (30).
x = 24/cos(30)
(cos(30) is the same as √3/2)
x = 24/√3/2
Step 1: Multiply by 2/√3
x = (24 * 2)/√3
Step 2: Rationalize the denominator by multiplying by √3
x = √3(24 * 2)/√3 * √3
Step 3: √3 squared is 3.
√3(24 * 2)/3
Step 4: Multiply 24 by 2 to get 48.
x = √3(48)/3
Divide √3(48) by 3 to get 16√3
x = 16√3
Before we figure out y, we need to find you what 16√3 squared is.
((16(√3))²
Step 1: Expand the above equation.
16²(√3)²
Step 2: Square 16 to get 256.
256(√3)²
Step 3: √3 squared is 3.
256(3)
Step 4: Multiply 256 by 3 to get 768.
768
Now, subtract 576 (24 squared) from 768 to get 192. Find the square root of that, which is 8√3. (192 = 8² * 3; rewrite as √8²√3, then take the square root of 8²