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