Sine Cosine and Tangent Practice Answer Key

Module 13 Review Identify the relationships in the figure to the right. 1. tan x = VW/WX 2. tan V = WY/WX 3. tan x * tan V = 1 4. WY/WX = m∠V Solve Problems 6-9 using tangent ratios and a calculator. Refer to the figure to the right of each problem. 6. To the nearest hundredth, what is tan m∠LMN? 0.72 7. Write a ratio that gives tan ∠S. 0.75/3.0. Find the value of tan ∠S to the nearest hundredth. 0.25. Use the inverse tangent function on your calculator to find the angle with that tangent. 14° 8. Write and solve a tangent equation to find the distance from C to E to the nearest 0.1 meter. 35.3 meters 9. The glide slope is the path a plane uses while it is landing on a runway. The glide slope usually makes a 3° angle with the ground. A plane is on the glide slope and is 1 mile (5280 feet) from touchdown. Find EF, the plane's altitude, to the nearest foot. Show your work.   277 ft After verifying that the triangle to the right is a right triangle, use a calculator to find the given measures. Give ratios to the nearest hundredth and angles to the nearest degree.   10. Use the Pythagorean Theorem to confirm that the triangle is a right triangle. 11. sin ∠1 = 3/6 = 0.50 12. sin ∠2 = 5.2/6 = 0.87 13. cos ∠1 = 5.2/6 = 0.87 14. cos ∠2 = 3/6 = 0.50 Use a calculator and trigonometric ratios to find each length. Round to the nearest hundredth. 15. [Image of a right triangle with sides labeled 11 and 14] BO = 17.46 cm 16. [Image of a right triangle with sides labeled 16 and 9] QP = 18.36 mm 17. [Image of a right triangle with sides labeled 17 and 8] ST = 5.66 ft Use sine and cosine ratios to solve Problems 18-20. 18. Find the perimeter of the triangle. Round to the nearest 0.1 centimeter. [Image of a right triangle with sides labeled 9.5 cm and 4.2 cm] Perimeter = 23.2 cm 19. To the nearest 0.1 inch, what is the length of the hypotenuse of the springboard shown to the right? 36.4 in [Image of a right triangle with sides labeled 10 in and 36 in] 20. What is the height of the springboard (the dotted line)? 10.0 in 21. Fill in the side lengths for these special right triangles with a hypotenuse of 1. Use decimals to the nearest 0.01, and be sure that your answers make sense, for example that the hypotenuse is longer than the 1   1. studyres.com studyres.com legs. [Image of a 30-60-90 triangle with hypotenuse 1] 0.50, 0.87 [Image of a 45-45-90 triangle with hypotenuse 1] 0.71, 0.71 Use special right triangle relationships to solve Problems 22-24. 22. If cos A = 0.28, which angle in the triangles to the right is ∠A? [Image of a right triangle with sides labeled 25 cm and 7 cm] ∠A is the angle opposite the 7 cm side. If sin B = 0.22, which angle is ∠B? ∠B is the angle opposite the 9 cm side. 23. What is EF, the measure of the longest side of the sail on the model? Round to the nearest inch. 32 in [Image of a right triangle with sides labeled 24 in and 7 in] What is the measure of the shortest side? 14 in 24. If the small sail is similar to the larger one and is 11 inches high, about how wide is it? 6 in [Image of two similar right triangles, one with sides labeled 20 in and 11 in, and the other with sides labeled 32 in and x in] Use a calculator and inverse trigonometric ratios to find the unknown side lengths and angle measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.   25. [Image of a right triangle with sides labeled 4 yd and 5 yd] AC = 5 yd m∠B = 53° m∠C = 37° 26. [Image of a right triangle with sides labeled 9 ft and 12 ft] DE = 14.94 ft EF = 11.17 ft 27. [Image of a right triangle with sides labeled 17 km and 8 km] GH = 19 km m∠H = 62° m∠G = 28° XYZ has vertices X(6, 6), Y(6, 3), and Z(1, 3). Complete Problems 28-30 to find the side lengths to the nearest hundredth and the angle measures to the nearest degree.   28. Plot the points and draw ∆XYZ. 29. Find XY and YZ from the graph. Use the Pythagorean Theorem to find XZ. XY = 3 YZ = 5 XZ = 5.83 30. Find the angle measures. m∠X = 59° m∠Y = 31° m∠Z = 90° For each triangle, find all three side lengths to the nearest hundredth and all three angle measures to the nearest degree.   31. B(-2, 4), C(8, 4), D(3, -2) BC = 8.66; BD = 7; CD = 5; m∠B = 30°; m∠C = 60°; m∠D = 90° 32. L(-1, -6), M(-1, 1), N(1, -1) LM = 7; LN = 7.28; MN = 2; m∠L = 29°; m∠M = 74°; m∠N = 76° 33. X(-4, 5), Y(-3, 5), Z(-3, 4) XY = 1; XZ = 1.41; YZ = 1; m∠X = 45°; m∠Y = 90°; m∠Z = 45°