Download 10SCI-Lesson09-TrigonometryRatiosInVectors

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