Question

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

216
216

14.7
14.7

15.3
15.3

234
234
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Answer 1

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

\[ a^2 + b^2 = c^2 \]

where:
- \( a \) is one leg of the triangle,
- \( b \) is the other leg,
- \( c \) is the hypotenuse.

In this case:
- The base (one leg) is \( a = 3 \).
- The hypotenuse is \( c = 15 \).
- We need to find \( b \) (the other leg).

Plugging the known values into the Pythagorean theorem, we have:

\[ 3^2 + b^2 = 15^2 \]
\[ 9 + b^2 = 225 \]

Next, we subtract 9 from both sides:

\[ b^2 = 225 - 9 \]
\[ b^2 = 216 \]

Now, we take the square root of both sides to find \( b \):

\[ b = \sqrt{216} \]

Calculating the square root gives:

\[ b \approx 14.7 \]

Rounding to the nearest tenth, the unknown side length is **14.7**.

So the correct response is:

**14.7**