Question
Use Pythagoren Theorem to find the missing length of a leg?
Imagine a right triangle. The slanted side on the left is labelled 15 m, the bottom side is labelled 9 m, and the side on the right is labelled a.
Imagine a right triangle. The slanted side on the left is labelled 15 m, the bottom side is labelled 9 m, and the side on the right is labelled a.
Answers
GPT-4o mini
In a right triangle, the Pythagorean theorem states that:
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse (the longest side), and \(a\) and \(b\) are the lengths of the other two legs.
In your triangle, the hypotenuse is 15 m, one leg (the bottom side) is 9 m, and we need to find the length of the other leg (which we will call \(a\)). According to the theorem, we can set up the equation like this:
\[
a^2 + 9^2 = 15^2
\]
Calculating the squares, we get:
\[
a^2 + 81 = 225
\]
Next, isolate \(a^2\) by subtracting 81 from both sides:
\[
a^2 = 225 - 81
\]
\[
a^2 = 144
\]
Now, take the square root of both sides to find \(a\):
\[
a = \sqrt{144}
\]
\[
a = 12
\]
Therefore, the missing length of the leg is \(12 \, \text{m}\).
\[
a^2 + b^2 = c^2
\]
where \(c\) is the length of the hypotenuse (the longest side), and \(a\) and \(b\) are the lengths of the other two legs.
In your triangle, the hypotenuse is 15 m, one leg (the bottom side) is 9 m, and we need to find the length of the other leg (which we will call \(a\)). According to the theorem, we can set up the equation like this:
\[
a^2 + 9^2 = 15^2
\]
Calculating the squares, we get:
\[
a^2 + 81 = 225
\]
Next, isolate \(a^2\) by subtracting 81 from both sides:
\[
a^2 = 225 - 81
\]
\[
a^2 = 144
\]
Now, take the square root of both sides to find \(a\):
\[
a = \sqrt{144}
\]
\[
a = 12
\]
Therefore, the missing length of the leg is \(12 \, \text{m}\).