In right triangle ABC, the hypotenuse AC has a length of 15 centimeters, and leg AB has a … — ACT

In right triangle $ABC$ , the hypotenuse $AC$ has a length of $15$ centimeters, and leg $AB$ has a length of $9$ centimeters. What is the length, in centimeters, of leg $BC$ ?

Answer: 12 centimeters

Answer

The length of leg

BC

12

centimeters.

The length of leg

BC

is found using the Pythagorean Theorem,

AB^2 + BC^2 = AC^2

. Substituting the given values gives

9^2 + BC^2 = 15^2

, which simplifies to

81 + BC^2 = 225

. Subtracting 81 from both sides yields

BC^2 = 144

. Taking the square root of 144 gives the correct length of 12 centimeters.

Step-by-Step Solution

Identify the given dimensions and apply the Pythagorean Theorem.

AB^2 + BC^2 = AC^2

For any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

Substitute the known values

AB = 9

and

AC = 15

into the equation.

9^2 + BC^2 = 15^2

The hypotenuse

AC

is the side opposite the right angle, and

AB

is one of the legs.

Simplify the squared terms.

81 + BC^2 = 225

Squaring 9 yields 81, and squaring 15 yields 225.

Isolate the unknown term by subtracting 81 from both sides.

BC^2 = 144

Subtracting 81 from both sides isolates

BC^2

on the left side of the equation.

Take the square root of both sides to solve for the leg length.

BC = 12

Taking the square root of 144 gives the side length, which must be positive.

Key Concept

Pythagorean Theorem

Question

Answer

Step-by-Step Solution

Key Concept

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