Question

The length of the hypotenuse of a right triangle is 7 feet, and the length of one leg is 4 feet. what is the length of the other leg to the nearest tenth of a foot

Answer 1

The length of the other leg to the nearest tenth of a foot is 5.7 feet.

What is Pythagorean theorem?

• A theorem in geometry: the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.
• The Pythagoras theorem equation is expressed as, $c^{2} = a^{2} + b^{2}$, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs.

We can use the Pythagorean Theorem to find the length of the other leg

$a^{2} + b^{2} = c^{2}$

"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.

So,

      $b^{2} = c^{2} - a^{2}$

        =  7² - 4²

  b = $\sqrt{49 - 16}$

  $b = \sqrt{33}$ ⇒ 5.7 feet

Therefore, the length of the other leg to the nearest tenth of a foot is 5.7 feet.

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