Use the Pythagorean Theorem Quick Check

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Question
Use the image to answer the question.

A right triangle shows the base with a value of 3, the hypotenuse on the left with a value of 15, and the perpendicular side to the base on the right with a question mark.

Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth.

(1 point)
Responses

234
234

216
216

14.7
14.7

15.3

Answer 1

To find the unknown side length of the right triangle using the Pythagorean Theorem, we use the formula:

$$a^2+b^2=c^2$$

where:

• $c$ is the length of the hypotenuse,
• $a$ and $b$ are the lengths of the other two sides.

In this triangle:

• The base (one side) $a=3$,
• The hypotenuse $c=15$,
• The perpendicular side $b$ is unknown.

Plugging the values into the Pythagorean theorem:

$$3^2+b^2={15}^2$$ $$9+b^2=225$$

Now, isolate $b^2$:

$$b^2=225-9$$ $$b^2=216$$

Now, take the square root to find $b$:

$$b=\sqrt{216}$$

Calculating the square root:

$$b\approx 14.7$$

Therefore, the nearest tenth value of the unknown side length is:

14.7