MBF3C



MBF3CThe Sine Law 184658023050500In any triangle, if you know an angle and the length of the opposite side, you can use the Sine Law to find any other side or angle.asin A=bsin B=csin C sin Aa=sin Bb=sin Ccor… a =b sin Asin Bor… A=sin-1a sin BbExample: In ΔABC, given that ∠B = 48°, ∠C = 25°, and side a = 36 cm. Find the length of b and c.38862004572025°CBAa = 36 cm48°b = ?c = ?0025°CBAa = 36 cm48°b = ?c = ?543560-868870525°CBA36 cm48°0025°CBA36 cm48°Sketch the problem and label the sides/angles. According to the Sine Law you need a ratio of the sine of an angle and its corresponding side. Currently you don’t have this, however, you do have two other angles…State the formulas that you will be using:angle + angle + angle = 180° ∠A + 48° + 25° = 180° ∠A = 180° - 48° - 25° ∠A = 107°And asin A=bsin B=csin C36sin 107°=bsin 48°=csin 25°Solve the equations separately:36sin 107°=bsin 48°and36sin 107°=csin 25°36 sin 48°sin 107°=band36sin?25°sin?107°=c28.0 cm = band15.9 cm = cAnswer in a Sentence to show that you know what the numbers mean. “The lengths of the other two sides of the triangle are 28.0 cm and 15.9 cm.”Practice QuestionsSolve for the given variable (correct to 1 decimal place) in each of the following:asin?35°=10sin?40°65sin?75°=bsin?48°75sin?55°=csin?80°2120900228600b75°CAB23.6 cm35°00b75°CAB23.6 cm35°152400228600a53°CAB36 cm46°00a53°CAB36 cm46°For each of the following diagrams write the equation you would use to solve for the indicated variable:437586694927c73°CAB14.2 m15°00c73°CAB14.2 m15°Solve for each of the required variables from Question #2.For each of the following triangle descriptions you should make a sketch and then find the indicated side rounded correctly to one decimal place.In ΔABC, given that ∠A = 57°, ∠B = 73°, and c = 24 cm. Find the length of bIn ΔABC, given that ∠B = 38°, ∠C = 56°, and a = 63 cm. Find the length of cIn ΔABC, given that ∠A = 50°, ∠B = 50°, and b = 27 m. Find the length of cIn ΔABC, given that ∠A = 23°, ∠C = 78°, and c = 15 cm. Find the length of aIn ΔABC, given that ∠A = 55°, ∠B = 32°, and a = 77 cm. Find the length of bIn ΔABC, given that ∠B = 14°, ∠C = 78°, and b = 36 m. Find the length of a SEQ CHAPTER \h \r 1 Solutions:1. (a) 8.9 units (b) 50.0 units (c) 90.2 units2. (a) asin?53°=36sin?81° (b) 23.6sin?35°=bsin?70° (c) 14.2sin?15°=csin?73°3. (a) 29.1 cm (b) 38.7 cm (c) 52.5 m4. (a) 30.0 cm (b) 52.4 cm (c) 34.7 m (d) 6.0 cm (e) 49.8 cm (f) 148.7 m ................
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