Pythagoras theorem, question in summary

Question

 

David kicks a football from the ground to a wall the ball travels 22 meters through the air and hits a point on the wall which is 256cm high, work out the distance David is away from the wall using Pythagoras theorem

Answer 1

So for this question it is important to first manke sure all of the units in the question are the same.  I would chnage the 22 meters to centimeters, giving you 2200 centimeters.  Therefore, you end up with a right angle with the hypotenuse being 2200cm and a height of 256cm.  This allows you to solve for the distance from the wall

 

a = 256cm (height)

b = distance from wall

c = 2200cm (distance ball is kicked)

 

c² = a² + b²

 

2200² = 256² + b²

 

b² = 2200² - 256²

 

b² = 4,840,00 - 65, 536

 

b² = 4,774,464

 

b = 2185.05 cm or 21.85 meters

Answer 2

Hi Kingsley, using the Pythagoras Theorem, a² + b² = c², we can find the distance David is from the wall.

 

Let a represent the the height of the wall, in meters, or 2.54 meters.

 

Let c represent the distance the ball travels through the air, or 22 meters.

 

We need to solve for b.

 

2.54² + b² = 22²

 

6.4516 + b² = 484

 

Subtract 6.4516 from both sides:

 

b² = 477.5484

 

b = 21.85 

 

Davide kicked the ball from 21.85 meters.

 

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