+773 In the diagram, ABCD is a square with side length 2, and ABE is an equilateral triangle with side length 2. Find CF.
+12 To solve this problem, let's approach it step-by-step:
In an equilateral triangle, the altitude (height) is given by the formula:
h = (s√3)/2, where s is the side length
For triangle ABE, the side length is 2, so the height is:
h = (2√3)/2 = √3
This height √3 is equal to BF in our diagram.
Now we have a right triangle BCF, where:
BC = 2 (side of the square)
BF = √3 (height of the equilateral triangle)
We can use the Pythagorean theorem to find CF:
CF² = BC² - BF²
CF² = 2² - (√3)²
CF² = 4 - 3
CF² = 1
Taking the square root of both sides:
CF = 1
Therefore, CF = 1.
