Question
Finding the missing side of the right triangle. Click Here for Help Video.
656565
979797
Answers
GPT-4o mini
To find the missing side of a right triangle, you can use the Pythagorean theorem, which states that:
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) and \( b \) are the lengths of the two legs of the triangle,
- \( c \) is the length of the hypotenuse (the side opposite the right angle).
If you have two sides of a right triangle and you're looking for the length of the third side, follow these steps:
1. **Identify your sides**: Determine which sides are known and which one is missing. If you're trying to find a leg's length (\( a \) or \( b \)), make sure you have the hypotenuse (\( c \)) and the other leg.
2. **Rearrange the formula**:
- If you're looking for a leg: \( a^2 = c^2 - b^2 \)
- If you're looking for the hypotenuse: \( c^2 = a^2 + b^2 \)
3. **Plug in known values**: Substitute the known lengths into the equation.
4. **Calculate**: Solve for the unknown side, taking the square root of the result if necessary.
If you provide the known lengths, I can help you with the calculations!
\[ a^2 + b^2 = c^2 \]
where:
- \( a \) and \( b \) are the lengths of the two legs of the triangle,
- \( c \) is the length of the hypotenuse (the side opposite the right angle).
If you have two sides of a right triangle and you're looking for the length of the third side, follow these steps:
1. **Identify your sides**: Determine which sides are known and which one is missing. If you're trying to find a leg's length (\( a \) or \( b \)), make sure you have the hypotenuse (\( c \)) and the other leg.
2. **Rearrange the formula**:
- If you're looking for a leg: \( a^2 = c^2 - b^2 \)
- If you're looking for the hypotenuse: \( c^2 = a^2 + b^2 \)
3. **Plug in known values**: Substitute the known lengths into the equation.
4. **Calculate**: Solve for the unknown side, taking the square root of the result if necessary.
If you provide the known lengths, I can help you with the calculations!
The Leg is 65 and the other leg is x and the other thing is 97
GPT-4o mini
To find the missing leg \( x \) of the right triangle where one leg is 65 and the hypotenuse is 97, you can use the Pythagorean theorem as follows:
The formula is:
\[
a^2 + b^2 = c^2
\]
Where:
- \( a \) is one leg (65),
- \( b \) is the other leg (which is \( x \)),
- \( c \) is the hypotenuse (97).
Substituting the values into the equation:
\[
65^2 + x^2 = 97^2
\]
Calculating the squares:
\[
4225 + x^2 = 9409
\]
Now, isolate \( x^2 \):
\[
x^2 = 9409 - 4225
\]
Perform the subtraction:
\[
x^2 = 5184
\]
Now, take the square root of both sides to find \( x \):
\[
x = \sqrt{5184}
\]
Calculating the square root:
\[
x = 72
\]
So, the missing leg \( x \) is 72.
The formula is:
\[
a^2 + b^2 = c^2
\]
Where:
- \( a \) is one leg (65),
- \( b \) is the other leg (which is \( x \)),
- \( c \) is the hypotenuse (97).
Substituting the values into the equation:
\[
65^2 + x^2 = 97^2
\]
Calculating the squares:
\[
4225 + x^2 = 9409
\]
Now, isolate \( x^2 \):
\[
x^2 = 9409 - 4225
\]
Perform the subtraction:
\[
x^2 = 5184
\]
Now, take the square root of both sides to find \( x \):
\[
x = \sqrt{5184}
\]
Calculating the square root:
\[
x = 72
\]
So, the missing leg \( x \) is 72.