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AA 13-1 Right Triangle Trigonometry Trigonometry: * The study of the relationship among the angles and sides of a right triangle. B hypotenuse A leg opposite of B leg adjacent to A leg opposite of A leg adjacent to B C Trigonometric Functions: * Ratios that use the sides of a right triangle. sine (sin) cosine (cos) tangent (tan) cosecant (csc) secant (sec) cotangent (cot) opp = hyp csc cos = adj hyp sec tan = opp adj cot sin hyp = opp hyp = adj = adj opp Special Right Triangles: 30˚- 60˚- 90˚ and 45˚ - 45˚ - 90˚ Domain of each trig. function is the set of all acute angles of a right triangle. 0 < < 90 You can use one trig. ratio to find the value of another. Always use what you are given when trying to solve a right triangle. 30˚ 2x x√ 3 x 45˚ x√2 45˚ 60˚ x x Solving a Right Triangle: * When you know two sides of a right triangles or one side and an acute angle, then you can find the measures of all of the sides and angles. angle of depression Angle of Elevation: * The angle we look up at. line of sight Angle of Depression: * The angle we look down from. angle of elevation Line of Sight: * The path that our eyes follow. 1. Find the values of the six trig. functions for angle G. H 32 24 F 3. Write an equation involving sin, cos, or tan that can be used to find the value of x. Then solve the equation. Round to the nearest tenth. 40 x G 12 60˚ 2. If tan A = 5 , find the value of csc A. 3 4. Solve ∆XYZ. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. Y Z 11 28˚ X 5. In order to construct a bridge across a river, the width of the river at that location must be determined. Suppose a stake is planted on one side of the river directly across from a second stake at the opposite side. At a distance 30 meters to the left of the stake, at an angle of 55˚ is measured between the two stakes. 13 - 1 Right Triangle Trigonometry p. 706 - 708 #13, 15, 16, 22, 24, 26, 30, 32, 34, 35, 38, 41 - 42, 49, 50, 56, 58 (17 problems) 6. A run has an angle of elevation of 15.7˚ and a vertical drop of 1,800 feet. Estimate the length of the run.