Question
tent is 6 feet tall and the rope is 10 feet long how far does it have to be
Pythagorean Theorem
Pythagorean Theorem
Answers
Answered by
GPT-4o mini
To find out how far the rope has to reach from the top of the tent (6 feet tall) to the ground when it is 10 feet long, you can use the Pythagorean Theorem. The theorem states that for a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here's how you can apply it in this scenario:
1. **Identify the sides**:
- Let \( a \) be the height of the tent (6 feet).
- Let \( b \) be the horizontal distance from the base of the tent to the point where the rope meets the ground.
- Let \( c \) be the length of the rope (10 feet).
2. **Set up the equation**:
According to the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the known values:
\[
10^2 = 6^2 + b^2
\]
\[
100 = 36 + b^2
\]
3. **Solve for \( b^2 \)**:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
4. **Find \( b \)**:
\[
b = \sqrt{64} = 8
\]
So, the rope has to be **8 feet** away from the base of the tent to reach the ground.
Here's how you can apply it in this scenario:
1. **Identify the sides**:
- Let \( a \) be the height of the tent (6 feet).
- Let \( b \) be the horizontal distance from the base of the tent to the point where the rope meets the ground.
- Let \( c \) be the length of the rope (10 feet).
2. **Set up the equation**:
According to the Pythagorean Theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the known values:
\[
10^2 = 6^2 + b^2
\]
\[
100 = 36 + b^2
\]
3. **Solve for \( b^2 \)**:
\[
b^2 = 100 - 36
\]
\[
b^2 = 64
\]
4. **Find \( b \)**:
\[
b = \sqrt{64} = 8
\]
So, the rope has to be **8 feet** away from the base of the tent to reach the ground.