Tennis Ball Distance
While walking down the street you are pondering today's Trigonometry lesson when you trip on a tennis ball.
You look behind yourself to find that it rolled 10 meters to the left of a pothole that is directly behind you.
The angle the ball rolled off in was 30 degrees.
How far away is the tennis ball from you right now?
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1 solution
This is a trigonometry problem, so first and foremost you should use the unit circle as your tool for solving it.
Using the unit circle, we should identify what exactly what we are finding the length of and what we know.
We can draw an isosceles triangle to connect the three points: the student, the ball, and the pothole.
For starters, we know we are looking for the distance between us and the tennis ball. We know the direction it went in and at what angle, and we know the length of the opposite side of the triangle (the line between the tennis ball and the pothole).
At this point, the trigonometry kicks in. Using SOH CAH TOA, you should realize that you have the Opposite side, and need the Hypotenuse. So if you take cosine of 30, you get sqrt(3)/2. Opposite over Hypotenuse, then, is 10/x. Using cross-multiplication, x * sqrt(3) is 20. If you divide by sqrt(3), you will find that x = 33.333.
An important thing to note is that the angle says 30 degrees, but the unit circle says sin(30) is 1/2. However, that is when the angle is off of the x-axis. This was off the y-axis, so you can use cosine instead in this case.