Hello Everybody 
I would like you all to help see if I completed this problem correctly:
Regina, is a fullback, or defender, for her soccer team. She kicked the ball from the corner of the sideline (denoted by A below) hard enough to reach 120 ft. toward the forward (denoted by B) so the forward could take a shot at the goal.
Did her kick reach the forward? Explain and show your calculations.
Ok. As you can see above, a right triangle is formed. So I used Pythagorean Thereom to find the hypotenuse:
\(\displaystyle \L\bold 12^2+35^2=c^2\)
\(\displaystyle \L\bold 144+1225=c^2\)
\(\displaystyle \L\bold 1369=c^2\)
\(\displaystyle \sqrt{1369}\to\L\bold 37=c\)
So the distance between the fullback and the forward is 37 yds and the kick will go 40 yds.
\(\displaystyle \L\bold 120ft.\to1440in.\to40yds.\)
So my answer is:
Yes, the distance from A to B is 37 yds while the kick can go 40 yds. so the kick will reach the forward since 40>37yds. The distance from A to B, the distance from B to the imaginary line formed by the left of the goal, and the lateral distance for the left of that point to point A form a right triangle so you can use pythagorean thereom and calculate the hypotenuse (the path of the ball) and figure if it shorter/longer than the ball's path.
Seem good?
I would like you all to help see if I completed this problem correctly:
Regina, is a fullback, or defender, for her soccer team. She kicked the ball from the corner of the sideline (denoted by A below) hard enough to reach 120 ft. toward the forward (denoted by B) so the forward could take a shot at the goal.
Did her kick reach the forward? Explain and show your calculations.
Ok. As you can see above, a right triangle is formed. So I used Pythagorean Thereom to find the hypotenuse:
\(\displaystyle \L\bold 12^2+35^2=c^2\)
\(\displaystyle \L\bold 144+1225=c^2\)
\(\displaystyle \L\bold 1369=c^2\)
\(\displaystyle \sqrt{1369}\to\L\bold 37=c\)
So the distance between the fullback and the forward is 37 yds and the kick will go 40 yds.
\(\displaystyle \L\bold 120ft.\to1440in.\to40yds.\)
So my answer is:
Yes, the distance from A to B is 37 yds while the kick can go 40 yds. so the kick will reach the forward since 40>37yds. The distance from A to B, the distance from B to the imaginary line formed by the left of the goal, and the lateral distance for the left of that point to point A form a right triangle so you can use pythagorean thereom and calculate the hypotenuse (the path of the ball) and figure if it shorter/longer than the ball's path.
Seem good?