Question

three baseball players are playing catch. bella is directly south of amelia and directly west of edgar. bella and edgar are 12 feet apart and edgar and amelia are 20 feet apart. how far apart are bella and amelia? feet submit

Explanation:

Step1: Recognize the right - triangle

Since Bella is directly south of Amelia and directly west of Edgar, triangle \(ABE\) (where \(B\) is Bella, \(A\) is Amelia, \(E\) is Edgar) is a right - triangle with \(BE = 12\) (one leg), \(AE=20\) (hypotenuse), and \(AB\) (the other leg) which we want to find.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Let \(a = BE = 12\), \(c = AE = 20\), and \(b = AB\). Then \(AB=\sqrt{AE^{2}-BE^{2}}\).
Substitute the values: \(AB=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}\) (using \(a^{2}-b^{2}=(a + b)(a - b)\)).
First, calculate \((20 + 12)(20 - 12)=(32)\times(8)=256\).
Then \(\sqrt{256}=16\).

Answer:

16