To determine if the forces are pulling at right angles to each other, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two legs (a and b).
The theorem can be expressed as: \[ c^2 = a^2 + b^2 \]
Given:
- \( a = 2.9 \)
- \( c = 4.2 \)
We can rearrange the equation to solve for \( b^2 \): \[ b^2 = c^2 - a^2 \]
Now we will calculate \( c^2 \) and \( a^2 \):
- \( c^2 = 4.2^2 = 17.64 \)
- \( a^2 = 2.9^2 = 8.41 \)
Now, we can find \( b^2 \): \[ b^2 = 17.64 - 8.41 \] \[ b^2 = 9.23 \]
Taking the square root to find \( b \): \[ b = \sqrt{9.23} \approx 3.0 \]
To the nearest tenth, the length of the other leg \( b \) is \( 3.0 \).
Thus, the answer is: 3.0