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Trigonometry

Learn triangle types, sides, angles, trigonometric functions. Understand Pythagorean Theorem, Special Triangles, Simplifying Radicals, and word problems. Homework assignments included.

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Trigonometry

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  1. Trigonometry Students will be able to use right triangle trig to solve everyday problems. Students will use sine, cosine, tangent and inverse trig functions to solve for missing side and angle measurements.

  2. Triangle Review What do you remember • Types • Names • Properties • What lengths make a triangle • How do we determine type • How are sides and angles related

  3. Did you remember 3 Sides Angles add to 180 Right, Acute, Obtuse, Scalene, Isosceles, Equilateral Sum of shorter 2 sides must be greater than longest Longest side across from largest angle, smallest and smallest

  4. Examples Can these lengths make a triangle, is yes what kind? 6,10,8 9,18,8 5,7,10 8,8,10 What type of triangle is the following?

  5. More Example Put the angle in order from largest to smallest Put the sides in order from longest to shortest

  6. Pythagorean Theorem and radicals Using Pythagorean Theorem to solve for a missing side Simplifying a radical Special Right Triangles 45-45-90 30-60-90

  7. Simplifying Radical • Make a prime factor tree • Circle prime numbers in pairs or groups of 2 • Write one number from each pair outside the radical and multiple if more than 1 number • Prime numbers that are not circled write back under the radical

  8. Or Another Way • Find 2 factors of the number, one of the factors being the largest perfect square • Square root the largest perfect square and write it outside the radical, other number should stay underneath

  9. Example

  10. 45-45-90 Right Isosceles Triangle Hypotenuse = Leg times square root of 2

  11. 30-60-90

  12. Homework Worksheet on these properties 9.2 Middle column, is it a triangle and what type 5.1 1-11 odd 6.9 pg 33 1-6 honors pg 35 8 and 9

  13. Trigonometry Can only be used with right triangles We will use it to find measures of missing sides and angles All angles in right triangles are ratios of two of the sides All similar triangles corresponding angles will have the same trig ratio

  14. Describing the Sides in relation to a right triangle We need to talk about a right triangle and the side relationships based on the angles given • Opposite side in relationship to angle using Across from the angle, does not touch the angle we are using • Adjacent side in relationship to angle using Touches the angle, not hypotenuse, connects angle to right angle • Hypotenuse Always the longest side, across from the right angle

  15. Trig Ratios and Right Triangles The sides of the triangle have names, but it depends on the angle you are looking from. From angle A – Blue From angle B – Red

  16. Trig Ratios The trigonometric value of an angle is related to a specific ratio of two of the sides of the triangle SOH CAH TOA

  17. Setting Up Trig Ratio You should be able to set up all 3 trig ratios from all the angles in a triangle Make sure you have correct angle and correct sides

  18. Examples Continued Do you notice any relationships between angles and trig ratio

  19. Homework Wkst on setting up trig ratios

  20. Finding Missing Sides To find the missing side of a triangle you need to set up a specific trig ratio based on angle given and side you want to find These will look similar to proportions

  21. Set up • Determine Trig ratio you are using What angle is given What side is given What side do you need to find Which trig ration does this match up with • Set up trig ratio – using what you determined about, there should be only 1 unknown, this is the work I need to see • Solve trig ratio – you need a calculator with the trig functions to do this What are some things you noticed when solving

  22. Calculator Make sure your calculator is set up in correctly Mode Degree Sides lengths should always be rounded to the nearest hundredth unless specified otherwise

  23. Examples

  24. Your work fro trig ratios is the set up of the trig ratio, everything else is done in your calculator Do you notice when you multiple or divide

  25. Homework Worksheet on 3 trig rations Make sure you show set up and label your answers

  26. Solving for Angles We can also use trig ratios to calculate angles measure in a triangle Similar idea to how we did sides for triangles • What angle are we solving for • What sides do we have in relationship to the angle • What trig ratio uses those sides • Substitute and solve, round to nearest degree

  27. Using calculator

  28. Examples

  29. Homework Worksheet Trig ratios finding angle measures Remember to round to the nearest degree for your lable

  30. Word Problems

  31. Problem Solving Angle of Depression – angle line forms with horizon, coming down Angle of Elevation – angle formed with horizon going up

  32. Example Continued • When an 18 ft ladder is leaning against a wall and it makes a 68 degree angle with the ground. How high up the wall does the ladder reach?

  33. Homework Due 4/10 or 4/11 depending on class Pg 644 4-22 even Pg 648 1-9 odd 10,11,12 Honors Magic Square pg 607 Due 4/14 4/15 depending on class

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