The distance from home plate to dead center field in a certain baseball stadium is 409 feet. A baseball diamond is square with a distance from home plate to first plate base 90 feet. How far is it from first base to dead center field?

Question

I also need help setting this up.

Answer 1

Since the diamond's diagonal is along the direction of travel, the angle between the direction and the baseline is 135°.

The distance from 2nf base to dcf = 409-90√2

Now use the law of cosines to find the unknown distance:

d^2 = (409-90√2)^2 + 90^2 - 2(409-90√2)(90)cos 135°
d = 351.18 ft

Answer 2

Thank you!