The quarterback was on the 5 yard line and 30 yards from the sideline. He throws a ball to the receiver on the 45 yard line who was 50 yards from the same sideline. How far did the quarterback throw the football to the ball?

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Answer 1 · 2017-11-07T13:24:54

See a solution process below:

We can solve this using the Pythagorean Theorem.

The Pythagorean Theorem states for a right triangle:

#c^2 = a^2 + b^2# or #c = sqrt(a^2 + b^2)#

From the picture below you can see we have a right triangle with:

#a = 45 - 5 = 40"yds"# (Quarterback on the 5 throws to the receiver on the 45)

and

#b = 50 - 30 = 20"yds"# (Quarterback 30 yards from the sideline and the receiver on the 50 yards from the sideline)

enter image source here

We can substitute the values into the formula and calculate #c#:

#c = sqrt((40"yds")^2 + (20"yds")^2)#

#c = sqrt(1600"yds"^2 + 400"yds"^2)#

#c = sqrt(2000"yds"^2)#

#c = 44.7"yds"# rounded to the nearest tenth.

Or

#c = sqrt(400"yds"^2 * 5)#

#c = 20sqrt(5)"yds"#