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If one leg of a triangle is 6 inches and the hypotenuse is 13 inches, what

is the length of the other leg?

User Amlwin
by
7.9k points

2 Answers

2 votes

Answer:

7 inches duhh

Explanation:

User Dpstart
by
7.7k points
5 votes

Answer:


\boxed {\boxed {\sf b \approx 11.53 \ in}}

Explanation:

Since this is a right triangle, we can use the Pythagorean Theorem.


a^2+b^2=c^2

In this theorem, a and b are the legs and c is the hypotenuse.

We are given one leg that is 6 inches and the hypotenuse is 13 inches. We don't know the other leg. Substitute the known values into the formula.


(6 \ in)^2+b^2=(13 \ in)^2

Solve the exponents.

  • ( 6 in)²= 6 in* 6 in= 36 in²


36 \ in^2+b^2=(13 \ in)^2

  • (13 in)²= 13 in*13 in= 169 in²


36 \ in^2+b^2=169 \ in^2

Now, solve for b (the unknown side) by isolating the variable. 36 square inches is being added. The inverse of addition is subtraction, so we subtract 36 from both sides.


36 \ in^2-36 \ in^2+b^2=169 \ in^2- 36 \ in^2


b^2=169 \ in^2- 36 \ in^2


b^2=133 \ in^2

b is being squared. The inverse of a square is the square root. Take the square root of both sides.


\sqrt {b^2}=\sqrt {133 \ in^2}\\


b=\sqrt {133 \ in^2}\\


b= 11.5325625947 \ in

Let's round to the nearest hundredth. The 2 (11.5325625947) in the thousandth place tells us to leave the 3.


b \approx 11.53 \ in

The length of the other leg is approximately 11.53 inches.

User GtAntoine
by
9.0k points

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