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
Okay, chandamuleyi, let's work through this bearing problem. Given Information: Angle POQ = 55^ (This is QOP in the triangle). OQ = QP (This means triangle OQP is an isosceles triangle). Bearing of Q from O is 060^. a) Find the bearing of O from Q. Step 1: Use the given bearing of Q from O. The bearing of Q from O is 060^. Step 2: Calculate the back bearing. To find the bearing of O from Q, we use the rule for back bearings. If the bearing is less than 180^, add 180^. If it's greater than 180^, subtract 180^. Since 060^ < 180^, we add 180^. Bearing of O from Q = 060^ + 180^ = 240^ The bearing of O from Q is: 240^ b) Find the bearing of P from Q. Step 1: Determine the angles within triangle OQP. Since OQ = QP, triangle OQP is an isosceles triangle with base OP. This means the angles opposite the equal sides are equal: QPO = QOP. We are given POQ = 55^, so QOP = 55^. Therefore, QPO = 55^. Step 2: Calculate the angle OQP. The sum of angles in a triangle is 180^. OQP = 180^ - ( QOP + QPO) OQP = 180^ - (55^ + 55^) OQP = 180^ - 110^ OQP = 70^ Step 3: Calculate the bearing of P from Q. We know the bearing of O from Q is 240^. This is the angle measured clockwise from the North line at Q to the line segment QO. From the diagram, the line segment QP is clockwise from the line segment QO. Therefore, to find the bearing of P from Q, we add OQP to the bearing of O from Q. Bearing of P from Q = Bearing of O from Q + OQP Bearing of P from Q = 240^ + 70^ Bearing of P from Q = 310^ The bearing of P from Q is: 310^ Last free one today — make it count tomorrow, or type /upgrade for unlimited.