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Algebra 2 Unit 8 13.1: Right Triangle Trigonometry Name: _______________________________________ Block: __________ Solve for missing ANGLE Solving for missing SIDES 1.) Given two angles, subtract from ________ to find the 3rd 1) Pythagorean Theorem: When given _____ _____________. 2) Special Right Triangle: _______________ & _______________ 3) Trigonometry: _____________________ ***Last resort because a results in a decimal which is __________ __________________ than a radical! 2) Trigonometry: The missing angle is usually referred to as ______________________. *Use the _________________ trig functions: Pythagorean Theorem: Only works with triangles **The _____________________ is across from the right angle and is always the ______________ side.** Practice: Find the measure of the third/missing side of the following triangles. Leave answers as radicals if necessary. NO DECIMALS! 1. 2. 3 4 3. 1016 12 GIVEN: One Side of a Right triangle and a Special Case Angle: 45˚, 30˚, or 60˚ Special Right Triangles: There are two special right triangles. Case 1: 45-45-90: ________________________________________________________ Example: 45 45 Case 2: 30-60-90: _______________________________________________________ Example: 30 30 60 60 Practice: Use special right triangles to determine the length of the missing sides. Leave your answers exact – NO decimals!!! 4. 5. **6. 60˚ 30˚ 7 45˚ 6 7. 8. 10 45˚ **9. 30˚ 12 8 45˚ Trig! Remember, when finding a side length, try Pthag. Thm. or a Special Right BEFORE trig! GIVEN: One Side of a Right triangle and a Non-Special Angle: (NOT 45˚, 30˚, or 60˚) ***Two Sides of a Right triangle and you need to find an angle The ratios formed by the sides have names/labels: Remember Soh Cah Toa sin = θ cos = tan = θ Write 3 basic trigonometric ratios for the following triangle. A sin = 3 cos = 5 θ sin A = sin B = cos A = cos B = tan A = tan B = 6 tan = B 4 C 3 3 Use a calculator to complete. REMEMBER TO BE IN ________________ MODE!!! 10) cos 22 _____ 11) sin 79 ____ 13) sin 54° = 16) sin 70° = 12) tan 43 _____ x 9 14) cos 20° = x 52 15) tan 35° = x 25 3 x 17) cos 54° = 14 x 18) tan 54° = 82 x Using Trig to Solve for missing sides Find the value of x & y to the nearest tenth. Show the trig ratio. 19. x = _________ 20. x = _________ 21. x = _____ y = _____ x 52 14 27 10 x 72 10 y Work: Using Inverse Trig to Solve for MISSING ANGLES _____________ _____________ _____________ All three inverse trig. functions are found on your calculator: Press 2nd and then select the trig. function you want to use! Solve for x. 22.) sin x° = 2 7 23.) cos x° = 10 17 24.) tan x° = 2 5 Examples: Solve for the missing angle using the two sides that are given: 25.) 26.) 27.) 10 52 3 5 17 12.5 x