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, Dert, let's solve the problem from the image with the correct formatting. Step 1: Identify the given information from the diagram. We have a triangle PQR. The length of side PR = 7.6 cm. The angle PRQ = 30^ is labeled in the diagram. Point S is on the side QR, and PS is shown as an altitude, meaning PSR = 90^. Step 2: Calculate PRQ. The value for PRQ is directly given in the diagram. PRQ = 30^ Step 3: Calculate PS. Consider the right-angled triangle PRS. We know the hypotenuse PR = 7.6 cm and the angle PRQ = 30^. We want to find the side PS, which is opposite to PRQ. We use the sine function: () = OppositeHypotenuse ( PRQ) = (PS)/(PR) Step 4: Substitute the known values and solve for PS. (30^) = (PS)/(7.6 cm) We know that (30^) = 0.5. 0.5 = (PS)/(7.6 cm) PS = 7.6 cm × 0.5 PS = 3.8 cm 3 done, 2 left today. You're making progress.