Question

A high school softball diamond is a square. Thedistance from base to base is 60ft. To the nearest foot,how far does the catcher throw the ball from home plateto second base?Use the 45°-45°-90° TriangleHid60 ftHypotenuse=V2. LegTheoremh=Sub

Answer 1

In this problem we know tht one side of the square is equal to 60, and we know that if an angle is part by the halve then the angle will be 45 degrees so we can draw an imaginari horizontal line to have a small triangle like this:

Now we can use the pythagorical theorem so where:

$\begin{gathered} h=60 \\ \text{leg}1=\frac{d}{2} \\ \text{leg}2=\frac{d}{2} \end{gathered}$

so:

$60^2=(\frac{d}{2})^2+(\frac{d}{2})^2$

Now we simplify ad solve for d so:

$\begin{gathered} 3600=\frac{d^2}{4}+\frac{d^2}{4} \\ 3600=\frac{2d^2}{4}=\frac{d^2}{2} \\ 3600\cdot2=d^2 \\ d=\sqrt[]{7200} \\ d=84.85 \end{gathered}$