Getting ready for right triangles and trigonometry

Let’s refresh some concepts that will come in handy as you start the right triangles and trigonometry unit of the high school geometry course. You’ll see a summary of each concept, along with a sample item, links for more practice, and some info about why you will need the concept for the unit ahead.

This article only includes concepts from earlier courses. There are also concepts within this high school geometry course that are important to understanding right triangles and trigonometry. If you have not yet mastered the Introduction to triangle similarity lesson, it may be helpful for you to review that before going farther into the unit ahead.

The Pythagorean theorem is $a^2+b^2=c^2$‍, where $a$‍ and $b$‍ are lengths of the legs of a right triangle and $c$‍ is the length of the hypotenuse. The theorem means that if we know the lengths of any two sides of a right triangle, we can find out the length of the last side. We can find right triangles all over the place—inside of prisms and pyramids, on maps when we're finding distance, even hiding inside of equilateral triangles!

For more practice, go to Use Pythagorean theorem to find right triangle side lengths.

Here are a few of the exercises where reviewing the Pythagorean theorem might be helpful:

For geometry, the square root function takes the area of a square as the input and give the length of a side of the square as an output. We'll use square root expressions when we use the Pythagorean theorem to find a side length. The trigonometric ratios for benchmark angles like $30\mathrm{°}$‍, $45\mathrm{°}$‍, and $60\mathrm{°}$‍ depend on square root expressions.

For more practice, go to Simplify square roots and Simplify square root expressions.

Here are a few of the exercises where reviewing square root expressions might be helpful.

Remember how there are right triangles hiding everywhere? To apply the Pythagorean theorem and trigonometry in context, we need to notice where the right angles are and think about what the hypotenuse and legs represent. Then we figure out where the measurements we have fit into the picture.

We don't have an exercise for this, because the best way to practice is by drawing your own diagrams on paper or your surface of choice!

Here are a few of the exercises where practicing visualizing right triangles might be helpful:

By the end of the unit, you should be able to find all of the unlabeled lengths and angle measurements in the diagrams, not just the ones we asked about. Come back at the end of the unit and see how much you've learned!