Trigonometry Required for Physics Problems

By Steven Holzner

Physics problems sometimes require you to have some trigonometry under your belt. To see what kind of trig you need, take a look at the figure, which shows a right triangle. The long side is called the hypotenuse, and the angle between x and y is 90 degrees.


Physics problems require you to be able to work with sines, cosines, and tangents. Here’s what they look like for the image:


You can find the length of one side of the triangle if you’re given another side and an angle (not including the right angle). Here’s how to relate the sides:


And here’s one more equation, the Pythagorean theorem. It gives you the length of the hypotenuse when you plug in the other two sides:


Practice questions

  1. Given the hypotenuse h and the angle theta in the diagram above, what is the length x equal to?

  2. 2.If x = 3 m and y = 4 m in the diagram above, what is the length of h?

Following are the answers to the practice questions:

  1. x = h cos theta

    Your answer comes from the definition of cosine.

  2. 5

    Start with the Pythagorean theorem:


    Plug in the numbers, and work out the answer: