Question 449093
{{{drawing(300,300,0,10,0,10,


triangle(2,2,8,8,2,6),
locate(2,2,H),
locate(8,8,B),
locate(2,6,P)


)
}}}


Suppose H = home plate, B = 1st base, P = pitcher's mound. We have the lengths HB = 90, HP = 60.5. Also, angle PHB = pi/4. From the law of cosines,


*[tex \LARGE BP^2 = HB^2 + HP^2 - 2(HB)(HP)\cos(\frac{\pi}{4})]


Replace all the values of HB, HP, etc. to find BP.