Pythagorean Theorem: Right Triangles - Pre Algebra

1. A hiker walks 5 miles north, then 12 miles east. How far is the hiker in a straight line from the start?

   13 miles. The paths are legs of a right triangle: $\sqrt{25 + 144} = 13$.

2. A 13 ft ladder leans against a wall with its base 5 ft from the wall. How high up the wall does it reach?

   12 feet, since $\sqrt{169 - 25} = \sqrt{144}$.

3. A right triangle has hypotenuse 17 and one leg 8. What is the other leg?

   15, since $\sqrt{289 - 64} = \sqrt{225}$.

4. A right triangle has legs 6 and 8. What is the length of the hypotenuse?

   10, since $\sqrt{36 + 64} = \sqrt{100}$.

5. A right triangle has hypotenuse 10 and one leg 6. What is the other leg?

   8, since $\sqrt{100 - 36} = \sqrt{64}$.

6. Which side of a right triangle is the hypotenuse?

   The side opposite the right angle. It is always the longest side.

7. What does the Pythagorean Theorem state for a right triangle with legs $a$ and $b$ and hypotenuse $c$?

   $a^2 + b^2 = c^2$.

8. A right triangle has legs 2 and 3. What is the exact length of the hypotenuse?

   $\sqrt{13}$, since $2^2 + 3^2 = 13$.

9. What is the length of the diagonal of a rectangle that is 80 m long and 60 m wide?

   100 meters. The diagonal is the hypotenuse: $\sqrt{6400 + 3600} = \sqrt{10000}$.

10. Which triangle is a right triangle: sides 7, 24, 25 or sides 6, 7, 9?

    Sides 7, 24, 25, because $49 + 576 = 625 = 25^2$. For 6, 7, 9: $36 + 49 = 85 \ne 81$.

11. A right triangle has legs 5 and 12. What is the length of the hypotenuse?

    13, since $\sqrt{25 + 144} = \sqrt{169}$.

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