Answer :
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, [tex]c^{2} = a^{2} + b^{2}[/tex], 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
[tex]a^{2} + b^{2} = c^{2}[/tex]
"a" and "c" represent the two legs of the triangle and "b" represents the perpendicular.
So,
[tex]b^{2} = c^{2} - a^{2}[/tex]
= 7² - 4²
b = [tex]\sqrt{49 - 16}[/tex]
[tex]b = \sqrt{33}[/tex] ⇒ 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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