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
You're on a roll — here's how to solve this geometry problem: a) Construct triangle PQR in which PQ = 8cm, angle QPR = 50° and angle PQR = 70°. Step 1: Draw a straight line segment PQ that is 8 cm long. Step 2: Place the protractor at point P and mark an angle of 50^ from PQ. Draw a ray from P through this mark. This ray will form the side PR. Step 3: Place the protractor at point Q and mark an angle of 70^ from QP. Draw a ray from Q through this mark. This ray will form the side QR. Step 4: The point where the two rays from Step 2 and Step 3 intersect is point R. You have now constructed PQR. b) Measure and write the length of PR. Since I cannot physically measure the constructed triangle, I will calculate the length of PR using the Sine Rule. Step 1: Find the third angle, PRQ. The sum of angles in a triangle is 180^. PRQ = 180^ - QPR - PQR PRQ = 180^ - 50^ - 70^ PRQ = 180^ - 120^ PRQ = 60^ Step 2: Apply the Sine Rule to find the length of PR. 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) In PQR, we want to find PR. We know PQ = 8 cm, PQR = 70^, and PRQ = 60^. Using the Sine Rule: (PR)/(( PQR)) = (PQ)/(( PRQ)) (PR)/((70^)) = 8\, cm(60^) Step 3: Solve for PR. PR = 8\, cm × (70^)(60^) Using approximate values for sine: (70^) ≈ 0.9397 and (60^) ≈ 0.8660. PR = 8\, cm × 0.93970.8660 PR = 7.5176\, cm0.8660 PR ≈ 8.6808\, cm Rounding to one decimal place, as is common for measurements: PR ≈ 8.7\, cm The length of PR is approximately 8.7\, cm. Drop the next question.