4.

Determine whether the forces in the pair are pulling at right angles to each other.

For the values a = 7.2 which is a leg of a right triangle, and value c = 11.1, which is the hypotenuse, find the length of the other leg, b, to the nearest tenth.

1 answer

To determine the length of the other leg \( b \) in a right triangle where \( a = 7.2 \) is one leg and \( c = 11.1 \) is the hypotenuse, we can use the Pythagorean theorem, which states:

\[ c^2 = a^2 + b^2 \]

We can rearrange this formula to solve for \( b^2 \):

\[ b^2 = c^2 - a^2 \]

Now we can plug in the values for \( a \) and \( c \):

\[ b^2 = (11.1)^2 - (7.2)^2 \]

Calculating \( (11.1)^2 \):

\[ (11.1)^2 = 123.21 \]

Now calculating \( (7.2)^2 \):

\[ (7.2)^2 = 51.84 \]

Now we substitute these values back into our equation for \( b^2 \):

\[ b^2 = 123.21 - 51.84 = 71.37 \]

Now we take the square root of both sides to find \( b \):

\[ b = \sqrt{71.37} \]

Calculating the square root:

\[ b \approx 8.4 \]

So, to the nearest tenth, the length of the other leg \( b \) is:

\[ \boxed{8.4} \]

Now, regarding the question of whether the forces in the pair are pulling at right angles to each other: since we have established that \( a \) and \( b \) are the legs of a right triangle and \( c \) is the hypotenuse, it follows that the forces represented by \( a \) and \( b \) are indeed acting at right angles to each other.