1. Trigonometry Right-Angled triangles

2. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use 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. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Trigonometry: What is it used for? 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 To find the length of a side

4. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Labeling the sides  The hypotenuse is opposite the right-angle The opposite is opposite the labeled angle The adjacent is the side next to the labeled angle

5. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use The trigonometric ratios The trigonometric ratios, sin, cos, tan are used when comparing particular side lengths.

6. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Calculator work (side length) Calculator steps: Sin30= Question:Evaluate: Refers to the length on the opposite Refers to the length on the hypotenuse Refers to the angle in the triangle Answer: 30 o 1 2

7. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Calculator work (angle size) Calculator steps: shift tan (1/4)= Question: Find  if tan  =¼ Refers to the length on the opposite Refers to the length on the adjacent Refers to the angle in the triangle Answer: 14.036…=14 o (2 sig figs) 14 o 1 4

8. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Sine (Side length) 25 o x 5 Step 1: Decide which trig ratio to use and set up the trig equation. Step 3: Use calculator to evaluate. Find the value of the unknown side. Step 2: Rearrange the equation. hypotenuse opposite

9. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Sine (Angle size)  3 5 Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Use calculator to evaluate. Find the value of the unknown angle. hypotenuse opposite shift sin (3/5) = (nearest degree)

10. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Cosine (Side length) 40 o x 10 Step 1: Decide which trig ratio to use and set up the trig equation. Step 3: Use calculator to evaluate. Find the value of the unknown side. Step 2: Rearrange the equation. hypotenuse adjacent

11. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Cosine (Angle size)  4.6 Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Use calculator to evaluate. Find the value of the unknown angle. 9 hypotenuse adjacent shift cos (4.6  9) = (nearest degree)

12. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Tan (Side length) 55 o 6 x Step 1: Decide which trig ratio to use and set up the trig equation. Step 3: Use calculator to evaluate. Find the value of the unknown side. Step 2: Rearrange the equation. adjacent opposite

13. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Tangent (Angle size)  4.6 Step 1: Decide which trig ratio to use and set up the trig equation. Step 2: Use calculator to evaluate. Find the value of the unknown angle. 8.2 adjacent opposite shift tan (4.6  8.2) = (nearest degree)

14. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use 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) 5  4.4

15. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Challenge 2 A kite is flying on the end of a string which is 24 m long. If the string makes an angle of 17 o 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) 17 0 24 m x

16. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use 40 o x 2.2 Challenge 3 A roof is in the shape of an isosceles triangle. The pitch of the roof is 40 o and the height of the roof is 2.2m. Find the length of the base of the roof. Step 1: Draw a diagram with the given information. Step 3: Decide which trig ratio to use. Step 4: Solve the trig equation. Step 2: Create a right angled triangle. y 2.2

17. Next slide Previous slide © Rosemary Vellar Challenge 3 angle side angle side angle side 2 1 Labeling sides Why trig? s i n c o s t a n angle side Trig ratios Calculator use Last slide Use the navigation buttons to repeat selected slides.