You’ve just picked up a ground ball at first base, and you see the other teams player running towards third base. How far do you have to throw the ball to get it from first base to third base, and throw the runner out?

Step-by-step explanation:

Diagonal of a Square

The baseball infield is a square of a side length of a=90 ft. From first base to 3rd base the ball must travel the length of the diagonal of the square.

We can calculate the diagonal of a square with the formula

Substituting:

Calculating:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32