Elena drops her pencil into her cup and notices that it just fits diagonally. The pencil is 17 cm long and the cup is 15 cm tall. The diameter of the cup is 8 cm.
What is the Pythagoras theorem?
The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
Elena drops her pencil into her cup and notices that it just fits diagonally. The pencil is 17 cm long and the cup is 15 cm tall.
Consider the pencil and cup just make a right angle triangle. If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
[tex]|AC|^2 = |AB|^2 + |BC|^2 \\\\|17|^2 = |15|^2 + |BC|^2 \\\\289 = 225 + |BC|^2 \\\\ |BC|^2 = 289 - 225\\\\ |BC|^2 = 64\\\\ |BC|^2 = \sqrt{64} \\\\BC = 8[/tex]
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