Introduction to trigonometry M. S. Martin Feb 2007

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

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

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 Tan 28° x = Now lets just look at that math's HYPOTENUSE OPPOSITE ADJACENT 28° 3.600m ?

Re-arrangement of the equation Tan 28° = OPP or ? ADJ 3.6 Same as, Tan 28° = OPP Apply cross multiplication 1 x opp = tan 28° x opp = tan 28° x = 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

Write the equation for the x° in the following triangles X°X° Tan x = Sin x = Cos x = X°X° Tan x = Sin x = Cos x =

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° ? m Cos 25° = ADJ HYP Cos 25° = HYP Re – arrange HYP = Cos 25° =

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

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

Use ‘Tan’ to calculate drop off Tan 30° = opposite side adjacent side Tan 30° = opposite side Tan 30° = opposite side 550 Re-arrange formula Opp side = tan 30° x 550 = 317mm Total drop off = = 337mm

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

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

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

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

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