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

14.7
14.7

15.3
15.3

216
216

234

Answer 1

To find the unknown side length in the right triangle using the Pythagorean Theorem, we can start with the theorem itself, which states:

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

where:
- \( c \) is the length of the hypotenuse,
- \( a \) and \( b \) are the lengths of the other two sides.

In this case, we have:
- \( c = 15 \)
- \( a = 3 \)
- \( b = ? \)

We will substitute \( a \) and \( c \) into the equation:

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

Calculating the squares:

\[
9 + b^2 = 225
\]

Now, we will isolate \( b^2 \):

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

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

\[
b = \sqrt{216}
\]

Now, we can calculate \( \sqrt{216} \):

\[
b \approx 14.7
\]

Rounding 14.7 to the nearest tenth, the final answer is:

**14.7**