In right triangle ABC, the hypotenuse AC has length 25, and leg AB has length 20. What is … — SAT

In right triangle $ABC$ , the hypotenuse $AC$ has length $25$ , and leg $AB$ has length $20$ . What is the length of leg $BC$ ?

Answer: 15

For any right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse (

a^2 + b^2 = c^2

). In right triangle

ABC

, the hypotenuse is

AC = 25

and one of the legs is

AB = 20

. Substituting these values into the theorem gives

20^2 + BC^2 = 25^2

, which simplifies to

400 + BC^2 = 625

. Subtracting

400

from both sides results in

BC^2 = 225

. Taking the square root of both sides gives the length of leg

BC

15

Set up the Pythagorean theorem equation for the right triangle.

AB^2 + BC^2 = AC^2

The Pythagorean theorem relates the lengths of the legs and the hypotenuse of any right triangle.

Substitute the known lengths of side

AB

and hypotenuse

AC

20^2 + BC^2 = 25^2

We plug in

20

for leg

AB

and

25

for hypotenuse

AC

Evaluate the squared terms.

400 + BC^2 = 625

Squaring

20

gives

400

, and squaring

25

gives

625

Isolate the variable term

BC^2

BC^2 = 225

Subtracting

400

from both sides of the equation yields

225

Find the length of side

BC

BC = 15

Taking the square root of

225

gives the positive length of leg

BC

Applying the Pythagorean theorem to calculate a missing leg length of a right triangle when the hypotenuse and one leg length are given.

Question