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Examples • Find the sine, cosine and tangent of angles A, B. • Bonus find the sine of angle C. Sin(A) = 5/13 Sin(B)= 12/13 13 Cos(A)= 12/13 Cos(B)= 5/13 Tan(A)= 5/12 A 12 Tan(B)= 12/5 Sin(C)= 1 B C 5 Right Triangle Trigonometry Geometry Mr. Calise Ex. 2: Solving a Right Triangle (h) • Solve the right triangle. Round decimals to the nearest tenth. g H 25° You are looking for opposite and 13 hypotenuse which is the sin ratio. J h G sin H = opp. hyp. h 13 sin 25° = Set up the correct ratio 13 Substitute values/multiply by reciprocal 13 13(0.4226) ≈ h 5.5 ≈ h Substitute value from table or calculator Use your calculator to approximate. Ex. 2: Solving a Right Triangle (g) • Solve the right triangle. Round decimals to the nearest tenth. cos G = H g 25° You are looking for adjacent and hypotenuse which is the cosine ratio. 13 adj. hyp. g 13 cos 25° = 13 13(0.9063) ≈ g 11.8 ≈ h Set up the correct ratio 13 Substitute values/multiply by reciprocal Substitute value from table or calculator Use your calculator to approximate. J h G Using Right Triangles in Real Life • Space Shuttle: During its approach to Earth, the space shuttle’s glide angle changes. • A. When the shuttle’s altitude is about 15.7 miles, its horizontal distance to the runway is about 59 miles. What is its glide angle? Round your answer to the nearest tenth. Solution: • You know opposite and adjacent sides. If you take the opposite and divide it by the adjacent sides, then take the inverse tangent of the ratio, this will yield you the slide angle. Glide = x° altitude 15.7 miles distance to runway 59 miles tan x° = opp. Use correct ratio adj. tan x° = 15.7 Substitute values 59 Key in calculator 2nd function, tan 15.7/59 ≈ 14.9 When the space shuttle’s altitude is about 15.7 miles, the glide angle is about 14.9°. B. Solution Glide = 19° altitude h • When the space shuttle is 5 miles from the runway, its glide angle is about 19°. Find the shuttle’s altitude at this point in its descent. Round your answer to the nearest tenth. distance to runway 5 miles tan 19° = opp. adj. tan 19° = h Substitute values 5 5 tan 19° = h 5 The shuttle’s altitude is about 1.7 miles. Use correct ratio 5 Isolate h by multiplying by 5. 1.7 ≈ h Approximate using calculator Drill: Find the height of the tree. 40o 50 feet