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Chapter 12 Right Triangle Trigonometry Review Notes: What is the saying that helps us remember the Trig Functions: SOH-CAH-TOA Which stand for: sin(x ) = Opp Hyp cos(x ) = Adj Hyp tan(x ) = Opp Adj If you look up from a horizontal, you measure the angle of elevation. If you look down from a horizontal, you measure the angle of depression. Illustrate the statement above: Use your trigonometric table to find the value of: *ROUND all answers to two decimal places 1) cos 23 = .92 2) tan 64 = 2.05 3) sin 52 = .79 4) tan 78 = 4.70 Use your trigonometric table to find the measurement of the angle whose: 5) cos A =0.94 m<A = 19.95° 6) sin B= 0.05 m<B = 2.87° 7) tan A =6.31 m<A = 80.99° 8) cos B= 0.69 m<B = 46.37° 9) sin A = 6/10 = 3/5 A 10 8 C 6 4 cos A = 8/10 = 4/5 B tan B = 8/6 = 4/3 Find x. 10) 11) 37 13 x Cos(20) = 7/x Sin(37) = 13/x x = 7.45 yd. X = 21.60 12) 13) x 15 15 x 40 11 yd Tan(40) = x/15 Cos(x) = 11/15 X = 12.59 X = 42.83° 14) 15) Tan(x) = 8/14 B 24 Sin(x) = 14/24 x = 35.69° 14 yd X = 29.74° 8 x x C 14 m A Complete each Question. Make sure you give a diagram, the equation and solution. 16) A tree casts a shadow of 30 meters when the angle of elevation to the sun is 20º. Find the height of the tree to the nearest meter. Diagram: Equation: Solution: 10.92 m Tan(20°) = x/30 x 20° 30 m 17) The angle of elevation from a ship to the top of a 42m lighthouse on shore is 36 degrees. To the nearest meter, how far away is the ship from shore? Diagram: Equation: Tan(36°) = 42/x Solution: 57.81 m 42 m 36° x 18) Kate is flying a kite. If the angle the string creates with the ground is 67 and the kite is 35 ft in the air. To the nearest foot how much string has Kate let out? Diagram: 35 ft Equation: Sin(67°) = 35/x Solution: 38.02 ft. x 67° 19) A 15-foot ladder is resting against a wall. If the base of the ladder is 5 feet from the base of the wall, then what angle is the ladder making with the ground? Diagram: Equation: Cos(x°) = 5/15 15 ft x° 5 ft. Solution: 70.53°