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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

14.7
14.7

234
234

216
216

15.3
15.3

Answer 1

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

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

Where:

• \(a\) and \(b\) are the lengths of the two legs of the triangle,
• \(c\) is the length of the hypotenuse.

In this case:

• The base \(a = 3\),
• The hypotenuse \(c = 15\),
• We need to find the perpendicular side, which we'll call \(b\).

Plugging in the values we have into the Pythagorean theorem gives us:

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

Calculating the squares:

\[ 9 + b^2 = 225 \]

Next, we subtract 9 from both sides:

\[ b^2 = 225 - 9 \]

\[ b^2 = 216 \]

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

\[ b = \sqrt{216} \]

Calculating the square root:

\[ b \approx 14.7 \]

Rounding to the nearest tenth, we conclude that the length of the unknown side is approximately 14.7.

Thus, the correct response is:

14.7