In right triangle ABC, the measure of angle B is 90^\circ. If the length of side AB is 6 a… — SAT

In right triangle $ABC$ , the measure of angle $B$ is $90^\circ$ . If the length of side $AB$ is 6 and the length of side $AC$ is 10, what is the length of side $BC$ ?

Answer: 8

Answer

The length of side

BC

is 8.

By applying the Pythagorean theorem to right triangle

ABC

, we have

AB^2 + BC^2 = AC^2

. Substituting the given values gives

6^2 + BC^2 = 10^2

, or

36 + BC^2 = 100

. Subtracting 36 from both sides gives

BC^2 = 64

, and taking the square root yields

BC = 8

Step-by-Step Solution

Identify the hypotenuse and the given leg in the right triangle.

The hypotenuse is

AC = 10

and the given leg is

AB = 6

The side opposite the

90^\circ

angle (angle

B

) is always the hypotenuse.

Apply the Pythagorean theorem.

AB^2 + BC^2 = AC^2

, which becomes

6^2 + BC^2 = 10^2

The Pythagorean theorem states that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse.

Solve for the unknown leg

BC

36 + BC^2 = 100 \implies BC^2 = 64 \implies BC = 8

Simplify the squares, subtract 36 from both sides, and find the principal square root of 64.

Key Concept

The Pythagorean Theorem

Question

Answer

Step-by-Step Solution

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