This worksheet is designed to help students learn and/or practice finding missing sides of a right triangle given an angle and one side.
I am teaching distance learning right now due to COVID-19 shutting our school down for the rest of the school year, and I have found that the topics/worksheets I present to my Algebra 2 students need to cover one concept at a time. Prior to this worksheet I did the "Pythagorean Practice" worksheet (posted on TPT) that has students finding missing sides of a right triangle using the Pythagorean theorem (answers are both rounded and simplified radicals). Now they are finding a missing side using trig. After this, I will present how to use trig to find the angles of a right triangle if you have two sides, and then tie all of the right triangle trig together.
Another thing I have found is that I need to give students a way to check their work as they progress through the worksheet, so I am making sure to provide scrambled answers at the end of each worksheet.
When I teach right triangle trig, I always approach it from a proportion perspective. After going over the famous "SOHCAHTOA" with my students, I then go through the step by step process of using trig to find a missing side. I first tell the students to label the sides with H for hypotenuse, O for side opposite the angle, and then A (Adjacent) for the remaining side. Students always get confused with the adjacent side, which is why I have them label this side last. They are usually pretty good about finding the hypotenuse and the opposite side.
Next, I have them circle what side they know and then what side they are trying to find, and figure out if they will use Tan, Sin or Cos. They then fill in the proportion (I pre-made proportions for the students, with the 1 filled in for under the trig sign/angle). They then solve the proportion (most students are very proficient at proportions by now).
I have found that even my lowest students can be successful at right triangle trig by following these steps (rewritten in step by step form):
1. Fill in H, O and then A on the sides
2. Circle the side you know and the side you want to find
3. Fill in the proportion with the correct trig sign and ratio
4. Solve the proportion
On the triangles that have all the angles filled in, I tell the students to pick an angle (not the right angle of course) to use and then go from there.
I have included an answer key with this.
Trigonometry allows us to find sides of triangles that we would not normally be able to find, by taking advantage of the sine, cosine, and tangent ratios.
Let’s restate the sine, cosine, and tangent ratios before we start on examples:
Definition: Let \(\theta \) be one of the acute angles of a right triangle. Then
\(\large \sin \theta = \LARGE \frac{{opposite leg}}{{hypotenuse}}\)
\(\large \cos \theta = \LARGE \frac{{adjacent leg}}{{hypotenuse}}\)
\(\large \tan \theta = \LARGE \frac{{opposite leg}}{{adjacent leg}}\)
Now that we have stated the three trigonometric ratios, we can look at our examples (there are also three reciprocal trigonometric ratios: cosecant, secant, and cotangent. For now though, we will only use the three main ratios).
Example: Find the missing side \(x\). Round to the nearest tenth.
Solution: Since \(x\) is the opposite leg, and \(16\) is the adjacent leg, we can use the tangent ratio to set up the equation
\(\tan 62^\circ = \Large \frac{x}{{16}}\)
Multiplying both sides by 16 gives
\(x = 16 \cdot \tan 62^\circ \approx 30.1\), rounded to the nearest tenth
The value \(30.1\) was obtained by computing \(16\tan 62^\circ \) in a calculator.
MAKE SURE your calculator is in degree mode!!!
Example: Find the missing side \(x\). Round to the nearest tenth.
Solution: Here \(x\) is the opposite leg, and \(17\) is the hypotenuse. Then we can use the sine ratio to set up the equation
\(\sin 15^\circ = \Large \frac{x}{{17}}\)
\(x = 17\sin 15^\circ \)
\(x \approx 4.4\), rounded to the nearest tenth
Remember to keep your calculator in degree mode! And remember to set up the appropriate trigonometric ratio for the situation!
Below you can download some free math worksheets and practice.