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
Step 1: Identify the given information. We are given a triangle PQR with: • Side PQ = 41.6 m • Side PR = 70 m • Angle PQR = 105^ Part (i): Calculate angle QPR. To find QPR, we first need to find PRQ using the Sine Rule. The Sine Rule states that for a triangle with sides a, b, c and opposite angles A, B, C: (a)/( A) = (b)/( B) = (c)/( C) Applying this to PQR: (PQ)/(( PRQ)) = (PR)/(( PQR)) Substitute the known values: (41.6)/(( PRQ)) = (70)/( 105^) Rearrange to solve for ( PRQ): ( PRQ) = (41.6 × 105^)/(70) Calculate the value: 105^ ≈ 0.9659258 ( PRQ) = \