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
Here's how to solve the problem: Problem 6: Calculate and , and then find the size of PQR to the nearest degree. Solution: The diagram shows a triangle PQR with an altitude from Q to PR. Let the foot of the altitude be M. We have two right-angled triangles: PQM and RQM. Given: PM = 9 MR = 23 QM = 10 PQM = RQM = PQR = + Step 1: Calculate using PQM. In PQM, the side opposite to is PM = 9, and the side adjacent to is QM = 10. We use the tangent function: () = oppositeadjacent = (PM)/(QM) () = (9)/(10) = ((9)/(10)) ≈ 41.987^ Step 2: Calculate using RQM. In RQM, the side opposite to is MR = 23, and the side adjacent to is QM = 10. We use the tangent function: () = oppositeadjacent = (MR)/(QM) () = (23)/(10) = ((23)/(10)) ≈ 66.501^ Step 3: Calculate PQR. The angle PQR is the sum of and : PQR = + PQR ≈ 41.987^ + 66.501^ PQR ≈ 108.488^ Step 4: Round PQR to the nearest degree. PQR ≈ 108^ The values are: ≈ 42.0^ (to one decimal place) ≈ 66.5^ (to one decimal place) The size of PQR to the nearest degree is 108^.