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SohCahToa

HSG-SRT.A.2
Answer Keys Here

Aligned To Common Core Standard:

High School Functions - HSF-TF.B.5

"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. This is a great way for use to remember the core trigonometric ratios and their use. Soh stands for the definition of sine. Sin is equal to the opposite over the hypotenuse. Cah represents the definitional value of cosine. Cosine is equal to the adjacent over the hypotenuse. Toa is used to remember the concept of tangent. Tangent is equal to the opposite over the adjacent. Remember that this only is applicable to right triangles, we can not assume these ratios apply to a three-sided geometric shape unless we are certain a right angle exists within it. Once you find that 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. We will use these worksheets to put SohCahToa into action and learn how to apply it to many different scenarios.

Printable Worksheets And Lessons


  • 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?


Homework Sheets

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.



Practice Worksheets

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.