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.
ScanSolve AI Answer
Hey odusinakabira, good to see you again. To solve this problem, we'll use trigonometry, specifically the Cosine Rule and Sine Rule, after visualizing the movements with bearings. a) Calculate the distance of Q from P. Step 1: Determine the angle at the base camp R. P moves on a bearing of 205° from R. Q moves on a bearing of 060° from R. The angle PRQ between their paths from R is the difference between these bearings. PRQ = 205^ - 060^ = 145^ Step 2: Apply the Cosine Rule to find the distance PQ. We have a triangle RPQ with sides RP = 20 km, RQ = 15 km, and the included angle PRQ = 145^. The Cosine Rule states: PQ^2 = RP^2 + RQ^2 - 2(RP)(RQ)( PRQ) PQ^2 = 20^2 + 15^2 - 2(20)(15)(145^) PQ^2 = 400 + 225 - 600(-0.81915) PQ^2 = 625 + 491.49 PQ^2 = 1116.49 PQ = sqrt(1116.49) ≈ 33.4139 km Rounding to the nearest whole number: PQ ≈ 33 km b) Calculate the bearing of Q from P. Step 3: Use the Sine Rule to find RPQ. To find the bearing of Q from P, we first need to determine an angle within RPQ. Let's find RPQ. The Sine Rule states: (RQ)/(( RPQ)) = (PQ)/(( PRQ)) (15)/(( RPQ)) = (33.4139)/((145^)) ( RPQ) = (15 (145^))/(33.4139) ( RPQ) = (15 × 0.57358)/(33.4139) ( RPQ) = (8.6037)/(33.4139) ≈ 0.25747 RPQ = (0.25747) ≈ 14.92^ Step 4: Calculate the bearing of Q from P. The bearing of P from R is 205°. The