Question
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.
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.
Answers
GPT-4o mini
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.
\[
c^2 = a^2 + b^2
\]
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.