Solve Applied Problems Using the Law of Cosines
-The distance from home plate to dead center field in Sun Devil Stadium is 406 feet. A baseball diamond is a square with a distance from home plate to first base of 90 feet. How far is it from first base to dead center field?
A) $348.2$ feet
B) $383.5$ feet
C) $473.9$ feet
D) $331.1$ feet

Question

Quizplus · Accepted Answer

To find the distance from first base to dead center field, we can use the Law of Cosines since we have a triangle formed by the distance from home plate to first base (90 feet), the distance from home plate to dead center field (406 feet), and the distance from first base to dead center field (which we are trying to find). The angle at home plate is 90 degrees because a baseball diamond is a square. Using the Law of Cosines: $c^2 = a^2 + b^2 - 2ab\cos(C)$, where $a = 90$, $b = 406$, and $C = 90^\circ$, we find $c = \sqrt{90^2 + 406^2}$ because $\cos(90^\circ) = 0$. This calculation gives us $c \approx 348.2$ feet.

Solve Applied Problems Using the Law of Cosines -The Distance 348.2348.2348.2

Solve Applied Problems Using the Law of Cosines
-The Distance $348.2$