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SOHCAHTOA Write down everything you know about triangles. Include any vocabulary related to triangles that you may have learned. Include Diagrams. Be Creative…. Write down everything you know about triangles. +three sides, three angles, three corners(vertex or vertices), not a good wheel, strongest shape, sum of all angles is 180 degrees, isoceles, scalene, equilateral, right angle, obtuse, acute, pythagoras theorem (a squared + b squared= c squared), only works on Right angled triangles, pie or cheese, pizza, toblerone, legend of zelda triforce, hypoteneuse, legs I like the Nick Name RATS! Imagine the pitcher stands at the pitcher’s mound at one of the acute angles. S/he throws the ball to the side which is opposite to him/her. opposite Pitcher’s Mound From the opposite side, the player throws the ball to the player at the hypotenuse. opposite 2 3 hypoteneuse 1 Pitcher’s Mound The player at the hypotenuse throws the ball to the last side of the triangle which is the adjacent. Opposite 3 2 Hypoteneuse 1 4 Adjacent Pitcher’s Mound Every right angled triangle has three sides labelled from a reference angle. Hypoteneuse Opposite Reference Angle Adjacent What happens if we move the reference angle? Discuss this with a partner? How does this change the labels on the sides? Reference Angle The adjacent and the opposite are switched! The Hypotenuse stays the same! Reference Angle Hypotenuse—doesn’t change! Adjacent Opposite Label all the three sides from the reference angle. A H H O A O A A opposite O sin hypoteneuse H adjacent A cos hypoteneuse H opposite O tan adjacent A length of opposite sin ANGLE NAME length of hypoteneuse length of adjacent cos ANGLE NAME length of hypoteneuse length of opposite tan ANGLE NAME length of adjacent Here is a quick way to remember the sides that correspond to each ratio. SOHCAHTOA S O H CAH T O A Have you noticed three buttons on your calculator? Sin Cos Tan These buttons relate to the three trig ratios we have shown from the RATS. Sin Cos Tan The calculator can calculate the ratio for any given angle instantly. Find the sin 98 °. You may need to determine if you press the sin button or enter 98 first. Try this on your calculator: Answer is: 0.990268068 Check to see if your calculator is in the wrong mode. Mode ✔ Right Mode: Degree, D, Deg ✗ Wrong Modes: Grad, Rad Find your Mode Button to change it to Degrees and try the question again. Sin Cos Tan Find the following ratios using your calculator to 4 decimals: sin 45°= 0.7071 cos 60°= 0.5 tan 57°= 1.5398 Sin-1 Cos-1 Tan-1 These buttons help you find the angle if you are given the trig ratio. I call this ‘going backwards’. Find the above buttons on your calculator. They may be above your sin/cos/tan keys. You may need to use a Second Function Key or another key to access these additional functions on your calculator. Sin-1 Cos-1 Tan-1 Let’s try the following example. Find the angle if: 4 sin B 5 Method 1: Enter 4 ⁄ 5 on your calculator and enter second function sin Method 2: Enter second function sin ( 4 ⁄ 5) on your calculator ANSWER: 53.13 degrees What are the three trig ratios from the reference angle. 5 3 4 3 sin 5 3 tan 4 4 cos 5 Find the three ratios from the following triangle. ✔ 14 12 8 8 sin 14 12 cos 14 8 2 tan 12 3 √ SOHCAHTOA Starting at the reference angle decide which two sides you have. Pick the trig ratio that uses those two sides. 7 O 7 sin A 15 15 H ✔ A Ask yourself: What sides do I have? Which Trig Ratio uses those two sides! 6 tanB 25 6 25 ✔ B Ask yourself: What sides do I have? Which Trig Ratio uses those to sides! 25 cos C 36 36 25 ✔ C 56 ° Find the missing side x. 20 X 56 ° Have: Hypoteneuse Need: Adjacent Use the Cosine Ratio 20 X x cos 56 20 56 ° 20 X x cos 56 20 x cos 56 20 x 11.18 56 ° 20 X Find the missing side x. x 12 35 ° What is the side you have and what is the side you need? Have: Opposite Need: Hypotenuse Use the Sine Ratio x 12 35 ° The ratio that uses both the O and the H is the sin ratio. 12 is the opposite side X is the hypotenuse 35 ° Now we can fill in the ratio: 12 sin 35 x 12 X 35 ° Now we can fill in the ratio: 12 sin 35 x 12 x 20.92 sin 35 Solve for x in the above equation by using the ‘Switcheroo’ If the side you are missing is in the NUMERATOR such as: x sin 43 12 Then multiply the two values together x=sin 43 x 12 If the side you are missing is in the DENOMINATOR such as: 7 cos 43 x Then use the ‘switcheroo’ to switch the cos 43 and the x Answer would be 7÷(cos 43) Case 1: Multiply Case 2: Switcheroo × ÷ I hope this was everything you needed to know about trigonometry!