In a right triangle, one leg (a) is 10 cm, and its hypotenuse (c) is 26 cm. Find b?

Question

asked Feb 7, 2021 28.8k views

1 Answer

Mark Plotnick · Answer 1 · 2021-02-11T04:30:16+0000

Answer:

$\boxed {\tt b=24 \ centimeters}$

Explanation:

This is a right triangle, so we can use Pythagorean Theorem.

a^2+b^2=c^2

a and b are the legs, while c is the hypotenuse.

One leg is 10 centimeters. The hypotenuse is 26 centimeters. Therefore,

$a= 10 \ cm \\c= 26 \ cm$

$(10 \ cm )^2+b^2=(26 \ cm)^2$

Solve the exponents.

$100 \ cm^2+b^2=(26 \ cm)^2$

$100 \ cm^2+b^2=676 \ cm^2$

Subtract 100 from both sides of the equation.

$100 \ cm^2- 100 \ cm^2+b^2=676 \ cm^2- 100 \ cm^2$

$b^2=676 \ cm^2 - 100 \ cm^2$

$b^2= 576 \ cm^2$

Take the square root of both sides of the equation.

$√(b^2) =√(576 \ cm^2)$

$b=√(576 \ cm^2)$

$b= 24 \ cm$

The other leg of the triangle is equal to 24 centimeters.