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TF011 - TF.01.1 Review of Right TF.01.1 Triangle...

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Unformatted text preview: TF.01.1 - Review of Right TF.01.1 Triangle Trigonometry, Sine Law and Cosine Law and MCR3U – Santowski 1 (A) Review of Right Triangles In a right triangle, the primary trigonometric ratios (which relate pairs of sides in a ratio to a given reference angle) are as follows: sine A = opposite side/hypotenuse side cosine A = adjacent side/hypotenuse side tangent A = adjacent side/opposite side recall SOHCAHTOA as a way of remembering the trig. ratio and its corresponding sides 2 (B) Examples – Right Triangle (B) Trigonometry Trigonometry Using the right triangle trig ratios, we can solve for unknown sides and angles: ex 1. Find a in ABC if b = 2.8, C = 90°, and A = 35° ex 2. Find A in ABC if c = 4.5 and a = 3.5 and B = 90° ex 3. Solve ABC if b = 4, a = 1.5 and B = 90° 3 (C) Review of the Sine Law If we have an acute triangle, we cannot use the primary trig ratios, so we must explore new trigonometric relationships. One such relationship is called the Sine Law which states the following: 4 (D) Examples Sine Law We can use these new trigonometric relationships in solving for unknown sides and angles in acute triangles: ex 4. Find A in ABC if a = 10.4, c = 12.8 and C = 75° ex 5. Find a in ABC if A = 84°, B = 36°, and b = 3.9 ex 6. Solve EFG if E = 82°, e = 11.8, and F = 25° There is one limitation on the Sine Law, in that it can only be applied if a side and its opposite angle is known. If not, the Sine Law cannot be used. 5 (E) Cosine Law The Cosine Law states the following: a² = b² + c² ­ 2bcCosA We can use the Cosine Law to work in triangles in which the Sine Law does not work ­ triangles in which we know all three sides and one in which we know two sides plus the contained angle. 6 (F) Examples Cosine Law We can use these new trigonometric relationships in solving for unknown sides and angles in acute triangles: ex 7. Find c in CDE if C = 56°, d = 4.7 and e = 8.5 ex 8. Find G in GHJ if h = 5.9, g = 9.2 and j = 8.1 ex 9. Solve CDE if D = 49°, e = 3.7 and c = 5.1 7 (G) Links For help with right triangle trig: http://id.mind.net/~zona/mmts/trigonometryRealms/introductio For help with the Sine Law http://www.themathpage.com/aTrig/law­of­sines.htm For help with the Cosine Law http://www.themathpage.com/aTrig/law­of­cosines.htm 8 (H) Homework AW Text Page 247, Q1­5 Page 249, Q,5,6 Page 252, Q,5,6 Nelson Text, p497­8, Q11­14 9 ...
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