## Find the Missing Angle Using Trigonometry

#### Aligned To Common Core Standard:

**High School Geometry** - HSG-SRT.D.11

How to Find Missing Angles Using Trigonometry -
We use different formulae 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.
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.
USING TRIGONOMETRY - besides employing standard formulae, we can also incorporate trigonometric ratios to calculate the missing angles of a triangle.
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]. These worksheets and lessons help students learn to find missing angles through the use of trigonometric functions and formulas.

### Printable Worksheets And Lessons

- 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.

#### 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.