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Math Analysis UNIT TT TRIANGLE TRIGONOMETRY REVIEW PROBLEMS I. Geometric Applications 1) Find the area of a decagon inscribed in a circle with a radius of 11 inches. 2) Find the measure for the included angle of a triangle that is created by sides with lengths of 36 and 10 units and has an area of 24 square units. 3) Find the lengths of the diagonals of an isosceles trapezoid if the bases of the trapezoid are 22 cm and 10 cm and the height of the trapezoid is 3 cm. 4) Find the area of the parallelogram shown. 5) Find the length of the diagonals of the parallelogram shown. 15 112 23 18 11 37 6) Find the area of the quadrilateral shown. 17 6 118 90 9 MPH/CR 10/08 7) Find the area of the quadrilateral shown. 15 8 100 115 10 1 Math Analysis II. Right Triangle Trigonometry 1) The sides of an isosceles triangle are 5, 10, and 10. Find the measures of its angles. 2) At a distance of 100 m, the angle of elevation to the top of a fir tree is 28. How tall is the tree? 3) If tan = 7/6, find the remaining five remaining trigonometric ratios for . Give exact answers. 4) A ladder leaning against a house makes a 17 angle with the ground. If the ladder is 20 feet long, what is the distance from the base of the ladder to the house? 5) A sonar operator on a cruiser detects a submarine at distance of 500 m and an angle of depression of 37. How deep is the submarine? III. The Ambiguous Case Determine the number of solutions for each of the triangles shown. Do not solve the triangles. 1) mC = 55, a = 11, c = 18 2) mA = 63, a = 3, b = 8 3) a = 5, b = 4, mB = 74 4) mC = 52, b = 8, c = 7 5) a = 9, c = 8, mA = 23 IV. Solving the Triangle Solve each of the following triangles. 1) mR = 75, mS = 45, t = 3 2) mA = 100, mC = 30, c = 8 3) a = 17, b = 10, c = 21 4) q = 6, r = 7, mP = 50 5) mX = 21.1, x = 6, y = 9 6) a = 10, b = 11, c = 12 7) mM = 11, n = 15, p = 6 MPH/CR 10/08 2