If an arc of 60° on circle A has the same length as an arc of 45° on circle B, what is the ratio of the area of circle A to the area of circle B?
Circle M radius R(M) = 1 | Circle N radius R(N) = [(L(A) * 8)/pi] / 2 = 4/3
Arc length L(M) = 2rpi = 1.047197551 | Arc length L(N) = L(M)
Circle M area A = 3.141592654 | Circle N area A = (4/3)2pi = 5.585053606
The ratio of the area of a circle M to the area of a circle N is: A / B = 9 / 16
One side of a triangle is one-third of the longest side. The third side is 13 feet less than the longest side. The perimeter is 85. Find all three sides.
"one side" = x "long side" = 3x "third side" = 3x - 13
x + 3x + 3x - 13 = 85
x = 14
sides of a triangle are 14, 42, and 29
Inside a square with a side length of 10, two congruent equilateral triangles are drawn such that they share one side and each has one vertex on a vertex of the square. What is the side length of the largest square that can be inscribed in the space inside the square and outside of the triangles?
Triangle height: h = √50
Triangle side: a = h / cos(30º)
Side of a small square: s = a * sin(15º)