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 are the steps to calculate the length of EF: Step 1: Calculate the lengths of EH and GH in the right-angled triangle GEH. Given GEH = 35^ and EG = 25.4 cm. EH = EG (35^) = 25.4 (35^) GH = EG (35^) = 25.4 (35^) Step 2: Calculate EGH. In GEH, the sum of angles is 180^. Since GHE = 90^: EGH = 180^ - 90^ - 35^ = 55^ Step 3: Calculate HGF. Given EGF = 120^. We know EGF = EGH + HGF. HGF = EGF - EGH = 120^ - 55^ = 65^ Step 4: Calculate the length of HF in the right-angled triangle GHF. We use the value of GH from Step 1 and HGF from Step 3. HF = GH ( HGF) = (25.4 (35^)) (65^) Step 5: Calculate the total length of EF. EF = EH + HF EF = 25.4 (35^) + (25.4 (35^)) (65^) EF ≈ 25.4(0.81915) + (25.4(0.57358)) (2.14451) EF ≈ 20.80641 + (14.57893) (2.14451) EF ≈ 20.80641 + 31.26850 EF ≈ 52.07491 cm Step 6: Round the answer to three significant figures. EF ≈ 52.1 cm Drop the next question.