SohCahToa is a mnemonic device that we use to remember the arrangement of the three fundamental trigonometric ratios. We use these ratios to help us evaluate triangles to find the measures of missing sides or angles. These ratios work off our understanding of the names given to sides of the triangle. The hypotenuse is always the easiest to spot because it is the longest and directly opposite the right angle. The opposite leg of the triangle is opposite one of the acute angles. The adjacent leg is right next to the acute angle. When we are equipped with three measures within these environments, we can pretty much figure out all the other measures which is what make triangles very unique shapes. We will use these worksheets to put SohCahToa into action and learn how to apply it to many different scenarios.
Aligned Standard: HSF-TF.B.5
- Using SohCahToa In Real World Problems Lesson- Coach Miller has a tree in his front yard and is wondering how tall it is. His friend loans him some surveying equipment and shows him how to use it. Coach Miller stands 80 feet from the tree and determines that the surveying equipment reads 55 degrees for him to see the top of the tree. How tall is the tree?
- Review Guided Lesson - We explore the skill in a basic angle problem and a story based scenario.
- Guided Lesson Explanation - A complete breakdown of the previous exercises for you. We will start by drawing it up. We can quickly see that we are looking for the opposite side.
- Practice Worksheet 1 - Find the value of the trigonometric ratio. Express answers as a fraction in lowest terms.
- Practice Word Problems - Example: Susan wants to make sure that her frame is perfectly square. All four of the sides measure 10 inches. If the frame is square what will the measure of the diagonal be?
- Word Problems Part 2 - Example: Wires are being used to hold a 10 foot pole perfectly vertical. If the wires are 15 feet long, what angle do the wires make with the ground?
- Answer Keys - These are for all the unlocked materials above.
We work through all of the skills that are related to this concept.
- Homework 1 - Find the value of the trigonometric ratio. Express answers as a fraction in lowest terms.
- Homework 2 - We will apply our use of charts to solve these.
- Homework 3 - Find the measure of the indicated side for each right triangle.
- Homework 4 - Find the value of angle.
Outside of one of these sheets, we are focused on angles.
- Practice 1 - This is all application to find missing angles.
- Practice 2 - We use the trig chart once again.
- Practice 3 - A practice problem is provided. We are looking for missing sides.
- Practice 4 - Round answers to the nearest whole number.
Math Skill Quizzes
We see what you have learned over this selection of lessons and practice sheets.
- Quiz 1 - We put angles into our cross hairs.
- Quiz 2 - The focus is on finding the value of the sides.
- Quiz 3 - We look inside for the value of the unknown angles.
- Quiz 4 - We apply our algebra skill to right angle trig functions.
What is the Meaning of SohCahToa?
"SohCahToa" is a mnemonic device that is often used to remember the defined values of the core trigonometric functions (sine, cosine, and tangent). This is probably the second most used mnemonic device in High School math, just behind PEMDAS. This is a great way for us to remember the core trigonometric ratios and their use.
Theta (Θ) is commonly used to define an angle of interest. Once you have two of the measures of a triangle, you can apply these functions to learn the remaining measures of the geometric shape.
Soh stands for the definition of sine. Sin is equal to the opposite over the hypotenuse.
We can sum this up mathematically with: sin (Θ) = opposite / hypotenuse.
Cah represents the definitional value of cosine. Cosine is equal to the adjacent over the hypotenuse.
In equation form: cos (Θ) = adjacent / hypotenuse.
Toa is used to remember the concept of tangent. Tangent is equal to the opposite over the adjacent.
In equation form: tan (Θ) = opposite / adjacent.
Remember that this only is applicable to right triangles, we cannot assume these ratios apply to a three-sided geometric shape unless we are certain a right angle exists within it. Once you find that you have an established right angle, everything about these ratios builds from it. Another consideration is to remember here is that the hypotenuse is always opposite the right angle. The adjacent side of the triangle is the side or leg that touches the angle but is not the hypotenuse. While you may think that SohCahToa only applies to trigonometry problems on paper or on your screen, this technique is used almost daily in all forms of structure fabrication and construction. People that are making something, use this technique often.