A gymnast circles a pommel horse by an angle of 50 degrees. Find the angle in radians giving the answer to one decimal place.
In this question, we’re given this angle of 50 degrees which we need to change into radians. Just like degrees, radians are unit of measure of angles. We can visualize this problem if we like. Here we have the pommel horse, and the gymnast is moving about this through an angle of 50 degrees. In order to work out 50 degrees in radians, we’ll need to remember some key conversions. The two most common ones are that 360 degrees is equal to two 𝜋 radians or that 180 degrees is equal to 𝜋 radians. We only really need to remember one of these as we can see how either multiplying both sides of the equation by two or dividing both sides of the equation by two would get us the other conversion.
So let’s use the fact that 180 degrees is equal to 𝜋 radians to work out the number of radians in 50 degrees. Rather than working out how we go from 180 to 50 degrees, it can be helpful to have an interim step. For example, we could work out one degree in radians. To go from 180 degrees, we must divide by 180. Therefore, we’ll need to do the same on the other side of this equation. So, one degree is equal to 𝜋 over 180 radians. Then, to go from this step of one degree to 50 degrees, we must multiply by 50, doing the same on the other side of the equation which give us 𝜋 over 180 multiplied by 50 radians. We can simplify this by taking out a factor of 10 from the numerator and denominator so we have a value of five 𝜋 over 18 radians.
It’s worth noting that there are other steps we could’ve taken. For example, instead of finding one degree in radians, we could’ve calculated 10 degrees. In order to go from 180 degrees to 10 degrees, we must have divided by 18. To go from 10 degrees to 50 degrees, we would multiply by five. So we’d need to do that on the other side of the equation, which gives us the same answer of five 𝜋 over 18 radians.
It’s most common when we’re working with radians to give our answer in terms of 𝜋. But this question asks us for the value to one decimal place, which means that we’ll need to use our calculators. Typing in the value of five 𝜋 over 18 gives us a decimal value of 0.87266 and so on radians. And when we’re rounding to one decimal place, we need to check our second decimal digit to see if it’s five or more. And as it is, our answer rounds up to 0.9 radians, and that’s the value for the angle of 50 degrees.