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Trigonometry

Trigonometry. Right-Angled triangles. Instructions for use. There are 9 worked examples shown in this PowerPoint plus information slides A red dot will appear top right of screen to proceed to the next slide.

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Trigonometry

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  1. Trigonometry Right-Angled triangles

  2. Instructions for use • There are 9 worked examples shown in this PowerPoint plus information slides • A red dot will appear top right of screen to proceed to the next slide. • Click on either the navigation bars below or to the left of screen to access the relevant slides.

  3. Trigonometry: What is it used for? • To find the length of a side • Some practical uses include: • Navigation (e.g., finding lost ships) • Construction industry • Finding heights of buildings • Finding pitch of a roof x • To find the size of an angle 

  4. Labeling the sides The opposite is opposite the labeled angle The hypotenuse is opposite the right-angle hypotenuse opposite  adjacent The adjacent is the side next to the labeled angle

  5. The trigonometric ratios The trigonometric ratios, sin, cos, tan are used when comparing particular side lengths.

  6. Question: Evaluate: Refers to the length on the opposite Answer: 2 1 Refers to the length on the hypotenuse Refers to the angle in the triangle 30o Calculator work (side length) Calculator steps: Sin30= So!

  7. Refers to the length on the opposite 1 Refers to the length on the adjacent 14o Refers to the angle in the triangle 4 Calculator work (angle size) Question: Answer: 14.036…=14o (2 sig figs) Find  if tan  =¼ Calculator steps: shift tan (1/4)= So!

  8. 5 x 25o opposite hypotenuse Sine (Side length) Find the value of the unknown side. Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Rearrange the equation. Step 3: Use calculator to evaluate.

  9. 5 3  opposite hypotenuse (nearest degree) Sine (Angle size) Find the value of the unknown angle. Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Use calculator to evaluate. shift sin (3/5) =

  10. adjacent hypotenuse Cosine (Side length) 10 40o Find the value of the unknown side. x Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Rearrange the equation. Step 3: Use calculator to evaluate.

  11. adjacent hypotenuse (nearest degree) Cosine (Angle size) Find the value of the unknown angle. 4.6 9  Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Use calculator to evaluate. shift cos (4.69) =

  12. opposite adjacent Tan (Side length) x 55o Find the value of the unknown side. 6 Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Rearrange the equation. Step 3: Use calculator to evaluate.

  13. opposite adjacent (nearest degree) Tangent (Angle size) 8.2  Find the value of the unknown angle. 4.6 Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Use calculator to evaluate. shift tan (4.68.2) =

  14. 5 4.4  Challenge 1 What angle will a 5 m ladder make with the ground if it is to reach 4.4 m up a wall? Step 1: Draw a diagram with the given information. Step 2: Decide which trig ratio to use. Step 3: Solve the trig equation. (nearest degree)

  15. 170 24 m x Challenge 2 A kite is flying on the end of a string which is 24 m long. If the string makes an angle of 17o with the vertical, find the height of the kite above the ground. Step 1: Draw a diagram with the given information. Step 2: Decide which trig ratio to use. Step 3: Solve the trig equation. (nearest metre)

  16. 2.2 40o 40o y x Challenge 3 A roof is in the shape of an isosceles triangle. The pitch of the roof is 40o and the height of the roof is 2.2m. Find the length of the base of the roof. 2.2 Step 1: Draw a diagram with the given information. Step 2: Create a right angled triangle. Step 3: Decide which trig ratio to use. Step 4: Solve the trig equation.

  17. Last slide Use the navigation buttons to repeat selected slides.

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