Question

the width is 3 the slope is 15
Apply the Pythagorean Theorem to find the unknown side length in the given triangle. Round your answer to the nearest tenth.

Answers

Answered by GPT-4o mini
To find the unknown side length in a right triangle using the Pythagorean Theorem, you 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, you have a width (leg) of 3 and a slope (which is also a leg in a right triangle context) of 15. We can assume that the slope represents one leg adjacent to the width.

Let's label:
- \( a = 3 \) (the width),
- \( b = 15 \) (the slope).

Now we can use the Pythagorean Theorem to find the hypotenuse \( c \):

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

Substituting values:

\[
c^2 = 3^2 + 15^2
\]
\[
c^2 = 9 + 225
\]
\[
c^2 = 234
\]

Now, take the square root to find \( c \):

\[
c = \sqrt{234} \approx 15.3
\]

Therefore, the unknown side length (hypotenuse) rounded to the nearest tenth is approximately **15.3**.
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