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Using the Pythagorean Theorem, find the length of a leg of a right triangle if the other leg is 8 feet long and the hypotenuse is 10 feet long. A. 12.81 B. 36 C. 6 D. 4√ 41

Respuesta :

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The Pythagorean Theorem tells us that [tex] a^{2}+b^{2}=c^{2}[/tex] where c is the hypotenuse and a and b are the other two sides. To solve for one of the shorter sides we need to rearrange:

[tex]b=\sqrt{c^{2}-a^{2}}[/tex]

We can then substitute known values, and solve:
[tex]b=\sqrt{10^{2}-8^{2}}[/tex]
[tex]b=\sqrt{100-64}[/tex]
[tex]b=\sqrt{36}[/tex]
[tex]b=6 feet[/tex]

The length of the unknown leg of a triangle is 6 feet long

Further Explanation:

Right triangle

  • A right triangle is a triangle with one of its angles being 90 degrees or right angle.
  • The triangle has two shorter sides making the right angle and the hypotenuse which is the longest side.

Scalene triangle

  • It is a triangle that with sides and angles that are not equal.
  • Area of a scalene triangle depends on the features of the triangle given.

Pythagoras Rule

  • According to Pythagoras rule, in a right angled triangle if the squares of the shorter sides are added then they are equivalent to the square of the hypotenuse.
  • That is; [tex]a^{2} + b^{2} =c^{2}[/tex], where a and b are the shorter sides while c is the hypotenuse.

In this case;

We are given;

Hypotenuse = 10 ft

One leg = 6 ft

Therefore, assuming the other leg is b; then

[tex]b^{2} =c^{2} -a^{2} \\b^{2} = 10^{2}-8^{2}  \\ = 100 -64 \\ = 36 \\b^{2} = \sqrt{36} \\b= 6ft[/tex]

Therefore; the length of unknown leg is 6ft

Keywords: Right triangle, Pythagoras rule

Learn more about:

  • Pythagoras theorem: https://brainly.com/question/13035995
  • Right triangle: https://brainly.com/question/13035995

Level; High school

Subject: Mathematics

Topic: Pythagoras theorem

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