15.

Question

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.