# Triangle Missing Angle Worksheets

There are so many different ways to find the measure of a missing angle within a triangle. It all comes down to taking a step back from where you are and seeing everything that is already known. If you have enough information, great you have your answer. If you do not have your answer, ask yourself what other measures can when determine based on what we were given. Calculate every measure you can and then go back and ponder your original problem. That is literally the way to progress through almost all geometry and trigonometry problems when the answer is not staring you in the face. These worksheets and lessons help students learn to find missing angles through the use of trigonometric functions and formulas.

### Aligned Standard: HSG-SRT.D.11

- Distance Formula Step-by-Step Lesson- We use Cosine to find the missing value here. Go over all the use SOH-CAH-TOA.
- Guided Lesson - Lots of missing parts on these right triangles. Find them ASAP!
- Guided Lesson Explanation - The way the problems are setup, it really doesn't take much to solve them.
- Practice Worksheet - A nice series of rapid fire questions for you on the topic here.
- Matching Worksheet - Match the missing values to problems. Seems easy, until you realize some values are very close.
- Find the Missing Angle Worksheet Five Pack - This is the real deal, as far as trig goes.
- Types of Angles Worksheet Five Pack - Use all of your knowledge of angle trigonometry to solve these little scavenger hunts; if you will.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

Find the missing values to make these answers correct.

- Homework 1 - Find the missing angle when you are given the following dimensions. BC = 6 ; AC = 12 ; Cos ____ = 6 / 12
- Homework 2 - You should start by evaluating what is missing in the system and go from there.
- Homework 3 - Which function best fits that angle?

### Practice Worksheets

Work with the dimensions to find all the missing pieces.

- Practice 1 - Note the points of the triangle before you make your assumption.
- Practice 2 - Don't get lost in your angles.
- Practice 3 - Where are things breaking down here.

### Math Skill Quizzes

See what strategies you use to find everything that is missing and lost.

- Quiz 1 - Two complementary angles measure y and 45°. How many degrees are there in y?
- Quiz 2 - Two vertical angles measure 5x and 150°. How many degrees are there in x?
- Quiz 3 - See if you can find those angles.

### How to Find Missing Angles Using Trigonometry

Triangles are one of my absolute favorite geometric shapes because you do not need much information to understand just about every feature found within it. We use different formulas to find out the missing sides or angles of a triangle. However, there are other easier mathematical approaches to solve a triangle. For instance, we know that the sum of a triangle is equal to 180 degrees. And in case you have a right-angle triangle, you know that one of the angles is 90 degrees. That means the sum of the remaining two angles has to be 90 degrees. With such information, you can easily calculate the missing angles.

A triangle consists of three sides. Normally those sides are labelled based on the angles that are formed at each of the vertices (where the sides meet). These letters represent the measure of the interior angles that are formed. But how do you find the missing angles without this information? The simplest answer is to use the other properties of the triangle. For example, using the sides of the triangle. The lengths of sides of a triangle are related to the magnitudes of the angles. We can also incorporate trigonometric ratios to calculate the missing angles of a triangle.

In the case of right triangles, where one of the interior angles is that good old perpendicular angle each side gets a specific name based on how it positioned. The side opposite the right angle is called the hypotenuse, the other two sides are often referred to as legs. These legs will have specific names when we begin to attempt to find the measures of missing angles. If a leg is directly opposite an missing angle of our interest, we refer to that side as opposite. This makes the other leg called the adjacent side, because it is located in an adjacent manner to the angle of interest.

When choosing an angle out of the two angles of a right-angle triangle, we first establish ratios of three sides with the angles. The side with the angle and reaches to 90-degree angle is known as the adjacent side. The side opposite to this angle is known as the opposite side. Lastly, the hypotenuse is always opposite to the right angle. Using these three definitions, we have established three ratios to define the angle in relation to the lengths of sides.

**Sine** - The ratio of the opposite side to the hypotenuse of the triangle [sinΘ = opposite/hypotenuse]

**Cosine** - The ratio of the adjacent side to the hypotenuse of the triangle [cos Θ = (adjacent )/hypotenuse]

**Tangent** - The ratio of the opposite side to the adjacent side of the triangle [tan Θ = opposite/adjacent].