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LESSON 9 Trigonometry Ratios In Vectors • We can break vectors down into x and y components, using trigonometric ratios and the Pythagorean Theorem. For multiple vectors, we can figure out the total x components and the total y components. If done properly, this method is a more realistic interpretation of an object’s motion. • PYTHAGOREAN THEOREM: The sum of the squares of the two shortest sides on a right angle triangle is equal to the square of the hypotenuse (the longest side). E.g. • PROBLEM: Determine the length of the hypotenuse (c). • PRACTICE: Determine the length of the hypotenuse (c). • You may have learned about trigonometric ratios in math class. These ratios are handy since they allow us to properly analyze right angle triangles. To measure the angles, use SOH CAH TOA. • Consider the following triangle. We can solve for θ using all of the above trigonometric ratios. • We can now combine the Pythagorean Theorem with trigonometric ratios to solve for simple displacement problems. We will need to draw a simple sketch of the vectors and use the tangent function. • PROBLEM: A fox runs 75 m [N] to find some food. It then runs 35 m [E] to drink some water. Find the fox’s resultant displacement. • PRACTICE: Bobby walks 8 m [W], then 15 m [S]. Find his resultant displacement and his distance. • PRACTICE: Judy drives 15.6 km [N] and then 24.6 km [E] to get to work. Calculate her distance travelled and her resultant displacement. • H.W. Worksheet 9