1. Introduction to trigonometry M. S. Martin Feb 2007

2. Basic trigonometry equations SIN = OPP HYP COS =ADJ HYP TAN =OPP ADJ Remember SOH, CAH, TOA deg° OPPOSITE ADJACENT HYPOTENUSE

3. Now lets look at the calculator Find these functions on the calculator. Sin, Cos, Tan

4. Now lets look at how we use the equations We will use an example of 28° and the right angle triangle opposite We know the degrees, we know the length of one side, but not the length of the opposite side ? So we can apply the ‘tan’ formula here Tan 28° = OPP or ? ADJ 3.6 We have to re-arrange the formula OPP = Tan 28° x 3.600 Tan 28° x 3.600 = 1.914 Now lets just look at that math's HYPOTENUSE OPPOSITE ADJACENT 28° 3.600m ?

5. Re-arrangement of the equation Tan 28° = OPP or ? ADJ 3.6 Same as, Tan 28° = OPP 1 3.600 Apply cross multiplication 1 x opp = tan 28° x 3.600 opp = tan 28° x 3.600 = 1.914 An easy way to remember for rearranging other formula’s is Think of a simple equation 4 = 8 2 Find the corresponding number to your formula and look at what you have to do to the other numbers Meaning, you want 8 so 4 x 2 = 8 If you wanted 2, 8 ÷ 4 = 2 X

6. Write the equation for the x° in the following triangles X°X° 6 9 8 Tan x = Sin x = Cos x = 686989686989 X°X° Tan x = Sin x = Cos x = 5 8 7 575878575878

7. Write the equation, then solve it 30° 50m ? Sin 30° = OPP HYP Sin 30° = OPP 50 Re-arrange OPP = Sin 30° x 50 = 25 25° ? 14.670m Cos 25° = ADJ HYP Cos 25° = 14.670 HYP Re – arrange HYP = 14.670 Cos 25° = 16.187

8. Now let’s look at how it relates to a building Firstly to calculate the drop off measurement in a roof frame

9. Drop off measurements Can you see the drop off measurement ? Can you see the relevent triangle ? Handout, Now lets look at a example

10. Use ‘Tan’ to calculate drop off Tan 30° = opposite side adjacent side Tan 30° = opposite side 400 + 110 + 40 Tan 30° = opposite side 550 Re-arrange formula Opp side = tan 30° x 550 = 317mm Total drop off = 317 + 20 = 337mm

11. Pitch and eave width will change the drop off – see below 30° 22½° Smaller Drop-off (Higher Wall) Smaller eaves width Drop-off Same Roof Pitch Drop-off Larger eaves width Larger Drop-off (Lower Wall) Larger Roof Pitch Smaller eaves width SAME WALL HEIGHT Smaller Roof Pitch Larger eaves width Same Wall Height

12. Exercises Calculate the drop off, assume 20mm for birdsmouth cut. 400 110, 40, 100 26° Tan 26° = opposite side 400 + 110 + 40 Tan 26° = opposite side 550 Re-arrange formula Opp side = tan 26° x 550 = 268mm Total drop off = 268 + 20 = 288 mm

13. Exercises Calculate the drop off, assume 20mm for birdsmouth cut. 350 110, 50, 90 22° Tan 22° = opposite side 350 + 110 + 50 Tan 22° = opposite side 510 Re-arrange formula Opp side = tan 22° x 510 = 206 mm Total drop off = 206 + 20 = 226 mm

14. Exercises Calculate the drop off, assume 20mm for birdsmouth cut. 300 110, 60, 100 36° Tan 36° = opposite side 300 + 110 + 60 Tan 36° = opposite side 470 Re-arrange formula Opp side = tan 36° x 470 = 341 mm Total drop off = 341 + 20 = 361 mm

15. Exercises Calculate the drop off, assume 20mm for birdsmouth cut. 250 110, 40, 90 32° Tan 32° = opposite side 250+ 110 + 40 Tan 32° = opposite side 400 Re-arrange formula Opp side = tan 32° x 400 = 250 mm Total drop off = 250 + 20 = 270 mm