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Finding sides and angles.notebook Trig Functions QS Grade:10 Subject:Geometry Date:Mar 09 Right angle triangles have special ratios we can use to find • missing sides • missing angles Finding sides and angles.notebook First, check that we have a right angle triangle Label the sides in relation to on of the two angles that are NOT 90o opposite hypotenuse adjacent Finding sides and angles.notebook Label the sides in relation to on of the two angles that are NOT 90o OR hypotenuse adjacent opposite The hypotenuse will always be across from the 90o angle we must identify the angle in question and label the two sides opposite and attached. How do we know? Finding sides and angles.notebook There are 3 trigonometric ratios sine of an angle = opposite side hypotenuse cosine of an angle = adjacent side hypotenuse tangent of an angle = opposite side adjacent side "nick names" SOH CAH TOA sin θ = opp/hyp S O/H cos θ = adj/hyp C A/H tan θ = opp/adj T O/A Finding sides and angles.notebook complete the trig ratios for the angle A 5 A 3 Sin Cos 4 Tan 1 In this triangle the side opposite <A is 3. True False B 5 3 C 4 A Finding sides and angles.notebook 2 In this triangle find sine A. Round to 4 decimal places. B 5 3 4 C 3 A In this triangle find Tan B. Round to the four decimal places if needed. A 0.75 C 1.3333 B .8050 D 0.6 B 5 3 C 4 A Finding sides and angles.notebook Finding a side Label the sides of the triangle Set up a ratio with the unknown side (try to put it on the top of the fraction: the numerator) B 25 30o C 4 x A Find the height of this tree to the nearest tenth. Tan 35o = opp / adj = x/20 x 35o 20 m Finding sides and angles.notebook Finding an angle Label the sides of the triangle Set up a ratio with the unknown angle B θ 25 15 A C 5 What is the angle of descent for the airplane that is approaching the airport, at 5000 ft up, and 20,000 feet away. A 3.93o B 14.0o C 5,000 ft 17.4o xo 20,000 ft D 75.96o Finding sides and angles.notebook You want to build a wheelchair ramp into your house, it has to go up 6 feet, and the maximum angle is 5o. 6 How far from the house must the ramp start ? 6 ft x 7 Find the angle of this roof. 12 xo 15 5o Finding sides and angles.notebook 8 Which formula uses 15 and 30 to find angle A? A Sine B Cosine C Tangent D Pythagorean Theorem A 30 26 C 9 15 B Find the measure of angle B? A 30 26 C 15 B Finding sides and angles.notebook 10 Find the measure of angle A? Round to the nearest whole number. A 30 B 60 C 90 D 45 A 30 26 C 15 Things to remember about triangles All the angles add up to 180o Trig and pythagorus only work for right angle triangles Area = b x h 2 Area = √(s)(s-a)(s-b)(s-c) B