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Lesson 42 - Review of Right Triangle Trigonometry

Lesson 42 - Review of Right Triangle Trigonometry. Math 2 Honors – Santowski. (A) Review of Right Triangle Trig.

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Lesson 42 - Review of Right Triangle Trigonometry

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  1. Lesson 42 - Review of Right Triangle Trigonometry Math 2 Honors – Santowski Math 2 Honors - Santowski

  2. (A) Review of Right Triangle Trig Trigonometry is the study and solution of Triangles. Solving a triangle means finding the value of each of its sides and angles. The following terminology and tactics will be important in the solving of triangles. • Pythagorean Theorem (a2+b2=c2). Only for right angle triangles • Sine (sin), Cosecant (csc or 1/sin) • Cosine (cos), Secant (sec or 1/cos) • Tangent (tan), Cotangent (cot or 1/tan) • Right/Oblique triangle Math 2 Honors - Santowski

  3. (A) Review of Right Triangle Trig • 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 & the cosecant A = cscA = h/o • cosine A = adjacent side/hypotenuse side & the secant A = secA = h/a • tangent A = adjacent side/opposite side & the cotangent A = cotA = a/o • recall SOHCAHTOA as a way of remembering the trig. ratio and its corresponding sides Math 2 Honors - Santowski

  4. (B) Examples – Right Triangle 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° Math 2 Honors - Santowski

  5. Examples – Right Triangle Trigonometry Math SL1 - Santowski

  6. Examples – Right Triangle Trigonometry Math SL1 - Santowski

  7. B c a A C b (C) Cosine Law • The Cosine Law states the following: • a² = b² + c² - 2bccosA • b2 = a2 + c2 - 2accosB • c2 = a2 + b2 - 2abcosC • We can use the Cosine Law to work in right and non-right triangles (oblique) in which we know all three sides (SSS) and one in which we know two sides plus the contained angle (SAS). Math 2 Honors - Santowski

  8. (D) Law of Cosines: A b Have: two sides, included angle Solve for: missing side c C B a c2 = a2 + b2 – 2 ab cos C (missingside)2= (one side)2+ (otherside)2 – 2(one side)(other side) cos(includedangle) Math 2 Honors - Santowski

  9. (D) Law of Cosines: A Have: three sides Solve for: missing angle b c C B a Side Opposite Missing Angle Missing Angle a2 + b2 – c2 2ab cos C = Math 2 Honors - Santowski

  10. B c=5.2 a=2.4 A b=3.5 C (E) Cosine Law - Examples • Solve this triangle Math 2 Honors - Santowski

  11. (F) Examples Cosine Law • We can use these new trigonometric relationships in solving for unknown sides and angles in acute triangles: • ex 1. Find c in CDE if C = 56°, d = 4.7 and e = 8.5 • ex 2. Find G in GHJ if h = 5.9, g = 9.2 and j = 8.1 • ex 3. Solve CDE if D = 49°, e = 3.7 and c = 5.1 Math 2 Honors - Santowski

  12. If we have a non right 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: (G) Review of the Sine Law Math 2 Honors - Santowski

  13. (G) Law of Sines: Solve for Sides Have: two angles, one side opposite one of the given angles Solve for: missing side opposite the other given angle A b c C B a Missing Side a sin A b sin B = Math 2 Honors - Santowski

  14. (G) Law of Sines: Solve for Angles Have: two sides and one of the opposite angles Solve for: missing angle opposite the other given angle A b c C B a a sin A b sin B Missing Angle = Math 2 Honors - Santowski

  15. (H) 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. Math 2 Honors - Santowski

  16. (H) Homework • Nelson S6.1 Math 2 Honors - Santowski

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