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
Welcome back zionenergy4 — missed you this week. Here's how to solve the problem: The problem asks to calculate something correct to 3 significant figures. The image shows a diagram with points P, Q, and R, and some given information: • |PQ| = 8 km • |QR| = 13 km • The bearing of Q from P is 050^. • The bearing of R from Q is 130^. We need to find the length of PR. Step 1: Determine the interior angle at Q. The bearing of Q from P is 050^. This means the angle from the North line at P, clockwise to PQ, is 50^. Since the North lines at P and Q are parallel, the alternate interior angle to the 50^ bearing at P is the angle between the North line at Q and QP. This angle is also 50^. The bearing of R from Q is 130^. This is the angle from the North line at Q, clockwise to QR. The interior angle PQR is the angle between QP and QR. PQR = 130^ - 50^ = 80^ Step 2: Apply the Cosine Rule to find the length of PR. We have a triangle PQR with two sides and the included angle: |PQ| = 8 km |QR| = 13 km PQR = 80^ Using the Cosine Rule: c^2 = a^2 + b^2 - 2ab C Here, PR^2 = PQ^2 + QR^2 - 2(PQ)(QR) ( PQR) PR^2 = 8^2 + 13^2 - 2(8)(13) (80^) Step 3: Calculate the value of PR^2. PR^2 = 64 + 169 - 208 (80^) PR^2 = 233 - 208(0.173648...) PR^2 = 233 - 36.1208... PR^2 = 196.8791... Step 4: Calculate PR and round to 3 significant figures. PR = sqrt(196.8791...) PR = 14.0313... km Rounding to 3 significant figures: PR ≈ 14.0 km The length of PR is 14.0 km. Send me the next one 📸