Question

solving real - world problems with 45° - 45° - 90° triangles
a baseball field is in the shape of a square. the distance between each pair of bases along the edge of the square is 90 feet. what is the distance between home plate and second base?
\boxed{} \sqrt{2} feet

Explanation:

Step1: Identify triangle type

The line from home plate to second base forms the hypotenuse of a 45°-45°-90° right triangle, where each leg is 90 ft.

Step2: Apply 45-45-90 triangle rule

In a 45°-45°-90° triangle, hypotenuse = leg $\times \sqrt{2}$.
<Expression>
$\text{Hypotenuse} = 90 \times \sqrt{2}$
</Expression>

Answer:

$90\sqrt{2}$ feet