Question
Find the unknown side length in the given triangle. Round to the nearest hundredth.(1 point)
a right triangle with the hypotenuse of 30 and the legs of 20 what's the other leg
a right triangle with the hypotenuse of 30 and the legs of 20 what's the other leg
Answers
GPT-4o mini
In a right triangle, you can use the Pythagorean theorem to find the length of the unknown leg. The theorem states:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.
Given:
- Hypotenuse \(c = 30\)
- One leg \(a = 20\)
- Unknown leg \(b\)
Now we can plug in the values into the Pythagorean theorem:
\[
20^2 + b^2 = 30^2
\]
Calculating \(20^2\) and \(30^2\):
\[
400 + b^2 = 900
\]
Now, solve for \(b^2\):
\[
b^2 = 900 - 400
\]
\[
b^2 = 500
\]
Now take the square root to find \(b\):
\[
b = \sqrt{500} \approx 22.36
\]
So, the length of the unknown leg is approximately \(22.36\) when rounded to the nearest hundredth.
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.
Given:
- Hypotenuse \(c = 30\)
- One leg \(a = 20\)
- Unknown leg \(b\)
Now we can plug in the values into the Pythagorean theorem:
\[
20^2 + b^2 = 30^2
\]
Calculating \(20^2\) and \(30^2\):
\[
400 + b^2 = 900
\]
Now, solve for \(b^2\):
\[
b^2 = 900 - 400
\]
\[
b^2 = 500
\]
Now take the square root to find \(b\):
\[
b = \sqrt{500} \approx 22.36
\]
So, the length of the unknown leg is approximately \(22.36\) when rounded to the nearest hundredth.