Math Pre-Calcul Quiz Review 6 Answers

Title: Pre-Calc 6.4-6.5 Quiz Review Header: Name Date (Key) Instructions: Use the Law of Sines to find the value of x. Problem 1: Triangle ABC with angles A = 35°, B = 114.4°, and C = 30.6° Side lengths: AB = x, BC = 17 Equation: sin(114.4)/x = sin(37.5)/17 Solution: x = 25.4 Problem 2: Triangle ABC with angles A = 67°, B = 40.3°, and C = 72.7° Side lengths: AB = 80.2, BC = 56.3, CA = x Equation: sin(67)/80.2 = sin(40.3)/56.3 Solution: x = 49.8 Problem 3: Triangle ABC with angles A = 30°, B = 50°, and C = 100° Side lengths: AB = 2, BC = a, CA = 1.3 Equation: sin(50)/2 = sin(30)/a Solution: a = 1.3 Problem 4: Triangle ABC with angles A = 80°, B = 31°, and C = 69° Side lengths: AB = 6.5, BC = 3.4, CA = c Equation: sin(80)/6.5 = sin(31)/3.4 Solution: c = 6.16 Problem 5: Triangle ABC with angles A = 22°, B = 95°, and C = 63° Side lengths: AB = 420, BC = c, CA = 1116.9 Equation: sin(22)/420 = sin(63)/c Solution: c = 998.98 Problem 6: Triangle ABC with angles A = 37°, B = 137°, and C = 6° Side lengths: AB = 30, BC = b, CA = 14.1 Equation: sin(37)/30 = sin(6)/b Solution: b = 14.1 Problem 7: Triangle ABC with angles A = 135°, B = 34.4°, and C = 10.6° Side lengths: AB = 100, BC = 80, CA = c Equation: sin(135)/100 = sin(10.6)/c Solution: c = 26.01 Problem 8: Triangle ABC with angles A = 50°, B = 100°, and C = 30° Side lengths: AB = 50, BC = 100, CA = c Equation: sin(50)/50 = sin(100)/c No solution Problem 9: Describes a scenario where points A and B are separated by a lake. A surveyor locates point C on land to measure the distance between A and B. Angle CAB = 48.6°, CA = 312 feet, CB = 527 feet. Uses the Law of Sines to find the distance between A and B. Solution: AB = 678.6 feet Problem 10: Triangle ABC with angles A = 108°, B = ?, and C = ? Side lengths: AB = 15, BC = 18, CA = x Uses the Law of Cosines to find the value of x. Solution: x = 26.8 Problem 11: Triangle ABC with angles A = ?, B = ?, and C = 130° Side lengths: AB = 10, BC = 12, CA = 20 Uses the Law of Cosines to find the value of x. Solution: x = 24.3 Problem 12: Triangle ABC with angles A = ?, B = ?, and C = 53° Side lengths: AB = 3.0, BC = 4.0, CA = ? Uses the Law of Cosines to find the value of x. Solution: x = 3.2 Problem 13: Triangle ABC with angles A = ?, B = ?, and C = 92.9° Side lengths: AB = 10, BC = 16, CA = ? Uses the Law of Cosines to find the value of x. Solution: x = 14.1 Problem 14: Triangle ABC with angles A = 60°, B = 35°, and C = 85° Side lengths: AB = 3, BC = ?, CA = x Uses the Law of Sines to find the value of x. Solution: x = 1.98 Problem 15: Triangle ABC with angles A = ?, B = ?, and C = 30° Side lengths: AB = 38, BC = 48, CA = x Uses the Law of Cosines to find the value of x. Solution: x = 24.3 Problem 16: Find the area of a triangle with side lengths of 9, 12, and 15. Uses Heron's formula to calculate the area. Solution: A = 54 square units Problem 17: Describes two straight roads diverging at an angle of 65°. Two cars leave the intersection at the same time, one traveling at 50 mph and the other at 30 mph. Finds the distance between the cars after 2:30 p.m. Uses the Law of Cosines to calculate the distance. Solution: distance = 23.1 miles Problem 18: A parallelogram has sides of length 3 and 5, and one angle is 50°. Finds the lengths of the diagonals. Uses the Law of Cosines to calculate the lengths of the diagonals. Solution: diagonal 1 = 3.8, diagonal 2 = 7.3 Problem 19: Two boats leave the same port at the same time, one traveling at 30 mph in the direction N 50° E and the other traveling at 26 mph in the direction S 70° E. Finds the distance between the two boats after one hour. Uses the Law of Cosines to calculate the distance. Solution: distance = 28.2 miles Problem 20: A boy is flying two kites at the same time, with 380 feet of line out to one kite and 420 feet to the other. Estimates the angle between the two lines to be 30°. Approximates the distance between the two kites. Uses the Law of Cosines to calculate the distance. Solution: distance = 210.6 feet Problem 21: Describes a tall building and two points A and B on the ground. From point A, the angle of elevation to the top of the building is 24.1°. From point B, which is 600 feet closer to the building, the angle of elevation is 30.2°. Finds the height of the building. Uses trigonometry to calculate the height. Solution: height = 1157.08 feet