Question

15.
Determine whether the forces in the pair are pulling at right angles to each other.

For the values a = 1.6 and b = 5.8, which are legs of a right triangle, find c, the hypotenuse, to the nearest tenth.

Answer 1

To determine whether two forces are pulling at right angles to each other, we first need to confirm that they can be represented as the legs of a right triangle. In this case, we have \( a = 1.6 \) and \( b = 5.8 \).

To find the hypotenuse \( c \) of the right triangle, we can use the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

Substituting the given values:

\[
c = \sqrt{(1.6)^2 + (5.8)^2}
\]

Calculating the squares:

\[
(1.6)^2 = 2.56
\]
\[
(5.8)^2 = 33.64
\]

Next, add these squares together:

\[
a^2 + b^2 = 2.56 + 33.64 = 36.20
\]

Now, take the square root of the total:

\[
c = \sqrt{36.20} \approx 6.0
\]

Thus, the hypotenuse \( c \) is approximately **6.0** when rounded to the nearest tenth.

Since the legs \( a \) and \( b \) are perpendicular to each other, the forces are indeed pulling at right angles to each other.