b c Pythagorean Theorem b) Find the value of the angle c) Evaluate cos 300

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1 Mathematis 11 Page 1 of Trigonometry Branh of mathematis hih deals ith triangle measurements. B a C A Si Trigonometri Ratios Primary Trig. Ratios Reiproal Trig. Ratios opp a sin A hyp adj os A hyp opp a tan A adj SOHCAHTOA Pythagorean Theorem? a a a? a Eample 1: Using a Calulator:?? (Make sure your alulator is in Degree mode) a) Evaluate os 60 ) Find the value of the angle ) Evaluate os 300 if os 0. a Eample 2: Solving a Right Triangle To solve a triangle means to find all the unknon sides and angles A 10 C 8 B Eample 3: Given the Value of One Trig. Ratio, find the values of the other to If tan, find the other to primary trigonometri ratios. RHHS Mathematis Department

2 Mathematis 11 Page 2 of Eample 4 A guy ire, 20 m long, supports a toer and forms an angle of 7 o ith the ground. a) At hat height to the nearest metre is the guy ire attahed to the toer? ) Ho far from the ase of the toer is the guy ire attahed to the toer? Eample Determine the measure of PS. O 10 m P R 3 m 60 o Q S RHHS Mathematis Department

3 Mathematis 11 Page 3 of Eample 6 A man hose eyes are 1.8 m aove the ground notes that the angle of elevation of the top of a uilding is 6. He alks 30 m farther aay and finds the angle of elevation to e. Ho tall is the uilding? Angle of Elevation Angle of Depression Alays from the HORIZONTAL!! RHHS Mathematis Department

4 Mathematis 11 Page 4 of SOLVING A RIGHT TRIANGLE Case 1 Given one angle and one side a) find the third angle using the angle sum in a triangle ) find the other to sides using the sine, osine, and tangent ratios Case 2 Given to sides a) find the third side using the Pythagorean Theorem ) find the measure of one angle using its sine, osine, or tangent ratio involving the given sides ) find the third angle using the angle sum in a triangle hek ith a trig ratio 1. Fill in the lanks. sin = hypotenuse adjaent = hypotenuse tan = 2. Calulate, to the nearest tenth of a metre. a) ) ) d) 43 3 m 28 m 0 6 m m 3. Calulate, to the nearest tenth of a entimeter. a) ) ) d) 17 m 27 m m m Calulate, to the nearest tenth of a degree. a) ) 21 ) d) Solve eah triangle. Round lengths to the nearest unit and angles to the nearest degree. a) ) ) d) 14 RHHS Mathematis Department

5 Mathematis 11 Page of 6. Determine the measure of BC, 7. Determine the measure of PO, to the nearest entimetre. to the nearest tenth of a metre. 8. Safety To guard against people falling, an etension ladder should make an angle of 7 or less ith the ground. What is the maimum height that an 8-m ladder an reah safely? 9. A ridge is 10 m aove the ater. From the ends of the ridge, the angles of depression of a uoy moored in the ater diretly elo the ridge are 32 o and 47 o. Find the length of the ridge. 10. From a point 0 m from the foot of a uilding, the angles of elevation of the top and ottom of the flagpole are 49 o and 46 o respetively. The flagpole is on top of the uilding. Find the height of the flagpole. 11. From to traking stations A and B, 30 km apart, a UFO is sighted at C aove AB making CAB = 32 o and CBA = 4 o. Find the height of the UFO.. From a oat on the ater, the angle of elevation of the top of a liff is 31 o. From a point 300 m loser, the angle of elevation is 33 o. Find the height of the liff. 13. From the top of a liff 18 m high, the angles of depression of to hannel uoys in the same line of sight on the ater are 13 o and 1 o. Ho far apart are the uoys? Ansers Opposite 1) Opposite, Cos, Adjaent 2a) 2.8 m ) 6.4 m ) 7.2 m d) 9.8 m 3a) 11.4 m ) 23.4 m ) 10.9 m d) 21.7 m 4a) 41.1 o ) 36.9 o ) 71.4 o d) 70.3 o a) r 14.3m; q 23.8m; P 3 ) l 28.8m; n 23.2m; N 39 ) a 6.2m; 3.3m; A 62 d) e 10.4mm; f 1.9mm; D 49 6) 166 m 7) 90.2 m 8) 7.7 m 9) 380 m 10) 13.8 m 11) 10km ) 2411 m 13) 111m RHHS Mathematis Department