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

14.7
14.7

216
216

15.3
15.3
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Answer 1

To find the unknown side length in the right triangle using the Pythagorean theorem, we can apply the following formula:

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

Where:
- \( a \) is one leg (base),
- \( b \) is the other leg (perpendicular side),
- \( c \) is the hypotenuse.

Given:
- \( a = 3 \) (base),
- \( c = 15 \) (hypotenuse),
- \( b \) is the unknown side.

Plug in the known values:

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

This simplifies to:

\[ 9 + b^2 = 225 \]

Now, subtract 9 from both sides:

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

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

\[ b = \sqrt{216} \]

Calculating the square root:

\[ b \approx 14.7 \]

Rounding to the nearest tenth, the answer is:

**14.7**