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Trigonometry Lecture Notes Section 2.4 Page 1 of 4 Section 2.4: Solving Right Triangles Big Idea: You can use trig functions and their definitions to compute missing measurements on a right triangle. Big Skill: You should be able to “solve” right triangles by computing missing measurements and stating your answers to the correct number of significant digits. The way we write a measurement can be used to indicate how precise the measurement was. o If we write 15 inches, that means the object we measured was between 14.5 and 15.5 inches long. o If we write 15.0 inches, that means the object we measured was between 14.95 and 15.05 inches long. o If we write 15.00 inches, that means the object we measured was between 14.995 and 15.005 inches long. o In other words, a measurement is good to ½ of the least significant digit. This is called using significant digits to write a number. When using trig functions, the rules for writing significant digits are as follows: Angle Precision 1 0.1 or 10 0.01 or 1 0.001 or 10 Angles and Accuracy of Trig Functions Trig Function Accuracy Example 2 sig. figs. sin17 0.29 , tan85 11 3 sig. figs. sin1.1 0.0192 , cos520' 0.996 4 sig. figs. cos 45.00 0.7071 , tan8013' 5.799 5 sig. figs. cos 45.000 0.70711 , tan801320 5.8028 To solve a right triangle: 1. Make a sketch of the triangle, label sides and angles consistently (a, b, and c for the legs and hypotenuse; A and B for the complementary angles), and label the given information. 2. Find a way to relate the unknown parts to the given information using: a. a trig function (sine, cosine, or tangent), b. the Pythagorean Theorem (a2 + b2 = c2), c. or complementary angles. d. Try to use original given information to minimize rounding errors. 3. Check your work: a. Make sure the sides obey the Pythagorean Theorem. b. Make sure the angles add up to 180. c. Make sure unused trig functions give the right answers. d. Make sure that the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle. Trigonometry Lecture Notes Section 2.4 Practice: 1. Solve a right triangle given two legs: 2. Solve a right triangle given a leg and a hypotenuse: Page 2 of 4 Trigonometry Lecture Notes Section 2.4 3. Solve a right triangle given an angle and an adjacent side: 4. Solve a right triangle given an angle and an opposite side: Page 3 of 4 Trigonometry Lecture Notes Section 2.4 5. Solve a right triangle given an angle and the hypotenuse: Page 4 of 4