In a right triangle, the length of the hypotenuse is denoted by c, and the lengths of the … — Armed Services Vocational Aptitude Battery (ASVAB)

In a right triangle, the length of the hypotenuse is denoted by $c$ , and the lengths of the two legs are denoted by $a$ and $b$ . If $a = 8\text{ cm}$ and $c = 17\text{ cm}$ , what is the length of leg $b$ ?

A
$9\text{ cm}$
B
$225\text{ cm}$
$15\text{ cm}$ Answer
D
$\sqrt{353}\text{ cm}$

Answer

The length of leg

b

15\text{ cm}

The Pythagorean theorem states that for any right triangle, the sum of the squares of the legs equals the square of the hypotenuse (

a^2 + b^2 = c^2

). By substituting

a = 8

and

c = 17

, the equation becomes

64 + b^2 = 289

. Subtracting

64

from both sides gives

b^2 = 225

. Taking the square root of

225

yields a leg length of

15\text{ cm}

Step-by-Step Solution

Identify the known and unknown values in the Pythagorean theorem formula.

Formula:

a^2 + b^2 = c^2

. Known:

a = 8

and

c = 17

. Unknown:

b

To ensure values are placed in the correct positions, specifically identifying

17

as the hypotenuse (

c

Substitute the known values into the equation and square them.

8^2 + b^2 = 17^2

becomes

64 + b^2 = 289

To simplify the equation before isolating the unknown variable.

Isolate

b^2

by subtracting

64

from both sides of the equation.

b^2 = 289 - 64

, which simplifies to

b^2 = 225

To get the squared unknown variable by itself on one side of the equals sign.

Take the square root of both sides to solve for

b

b = \sqrt{225} = 15\text{ cm}

To remove the exponent and find the final linear length of the leg.

Key Concept

Pythagorean Theorem and Variable Substitution

Estimated Time:1m 0s

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