Mathemadness

➕ Sines of Madness ➕

You're probably wondering why there are little buttons on your calculator reading 'sin' and 'cos'. There's also 'tan', but that's for later. These buttons are "sine" and "cosine" respectively.

You're also probably wondering what use that has. Well, here we go.

Say you're looking at a wheelchair ramp. You know the angle is 30 degrees, and the ramp itself is 25 feet long. You don't know how much the ramp elevates, and you don't have a tape measure. But you're able to find that out using only these pieces of info and some math! Here, we'll use the sine function.

Sine uses the lengths of two sides of a right triangle and an angle. You only need to know two of these values to determine the third. In this case, the function uses both the ramped side (or the hypotenuse, in math-y terms) and the side opposite of the angle.

This picture shows what we know about the ramp. The side opposite of the angle we know is labeled x, because we don't know what it is.

The sine formula is very straightforward.

So, we can take this formula and fill in the holes.

You're probably wondering how I changed sin (30) into 1/2. Well, by typing that into your calculator, you can know what the sine of 30 is, so you can replace it with a much easier algebra problem. Because of sine, we found out that the height of the ramp is 12.5 feet.

Cosine is very similar. The formula is the exact same except it uses the side adjacent to the angle.

But there's also a 'tan' button, too! Shouldn't that be similar, too?

---This chapter has concluded. You can use this as a little bookmark to stop and come back later. Maybe add a little time in between some chapters to breathe, get a drink or do some research on your own! The time is yours to spend.---