A baseball diamond is a square 63 feet on a side. The pitcher's mound is located on a line joining home plate and second base, 47 feet from home plate. If the pitcher is facing home plate, through what angle does he need to turn to face third base?
Please someone help, i know im missing some stupid rule about a square and its properties, but i cant seem to figure this out. I googled this problem and its normaly 90 feet for all sides. And the angle i cant envision properly. I believe its a pytharogean therom and then the law of sine/cosine to get the answer.
+129839 The distance to the middle of the square from home plate = 63/√2 ≈ 44.55 ft
So.....we figure the angle thusly [ it will be < 90° ]
Distance picther is from 3rd [using Law of Cosines]
D^2 = 63^2 + [63/√2]^2 - 2(63)(63/√2)cos (45)
D = √[ 63^2 + [47]^2 - 2(63)(47)cos (45) ] ≈ 44.615 ft
So we can use the Law of Sines to find the angle, θ
sinθ/ 63 = sin45 / 44.615 → sinθ = 63 * sin45 / 44.615
arcsin [ 63 * sin45 / 44.615 ] = θ ≈ 86.85°
Here's a pic :
