This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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You're on a roll — here are the solutions to the problems: Q8: Solve triangle ABC Step 1: Find angle A. The sum of angles in a triangle is 180^. Given B = 21^ and C = 46^. A = 180^ - B - C A = 180^ - 21^ - 46^ A = 113^ Step 2: Use the Sine Rule to find side a. The Sine Rule states (a)/( A) = (b)/( B) = (c)/( C). We are given c = AB = 9 cm. (a)/( A) = (c)/( C) a = (c A)/( C) a = (9 113^)/( 46^) Using approximate values: 113^ ≈ 0.9205 and 46^ ≈ 0.7193. a = (9 × 0.9205)/(0.7193) a ≈ (8.2845)/(0.7193) a ≈ 11.52 cm Step 3: Use the Sine Rule to find side b. (b)/( B) = (c)/( C) b = (c B)/( C) b = (9 21^)/( 46^) Using approximate values: 21^ ≈ 0.3584 and 46^ ≈ 0.7193. b = (9 × 0.3584)/(0.7193) b ≈ (3.2256)/(0.7193) b ≈ 4.48 cm The solved triangle has: Angle A = 113^ Side a ≈ 11.52 cm Side b ≈ 4.48 cm Q9: True Bearing of the following diagrams Step 1: Determine the true bearing for Diagram 1. The angle is 60^ clockwise from North. True Bearing = 060^ Step 2: Determine the true bearing for Diagram 2. The angle is 20^ from South towards West. True bearing is measured clockwise from North. From North to South is 180^. Adding 20^ towards West from South gives: True Bearing = 180^ + 20^ = 200^ Step 3: Determine the true bearing for Diagram 3. The angle is 30^ from North towards West (counter-clockwise from North). To find the true bearing (clockwise from North): True Bearing = 360^ - 30^ = 330^ Q10: Man's displacement Step 1: Analyze the first movement. The man travels West for 80 Km from town A. His position is 80 Km West of A. Step 2: Analyze the second movement. He then travels East for 100 Km. This movement is in the opposite direction to the first. Step 3: Calculate the net displacement. Let West be negative and East be positive. Net displacement = -80 Km + 100 Km Net displacement = 20 Km Step 4: State the final position and direction. Since the net displacement is positive, he is East of town A. He is 20 Km East from town A. Got more? Send 'em!