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
The question asks about triangle EFG, which has a right angle at F. Side EF is given as a, and angle G is . Since the specific question is not visible, I will assume you need to express the lengths of the other two sides, FG and EG, in terms of a and . Step 1: Identify the knowns and unknowns in relation to angle . In the right-angled triangle EFG: • Angle F is 90^. • Side EF is opposite to angle G, so opposite = a. • Side FG is adjacent to angle G, so adjacent = FG. • Side EG is the hypotenuse, so hypotenuse = EG. • Angle G is . Step 2: Express side FG using the tangent ratio. The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. () = oppositeadjacent Substitute the known values: () = (EF)/(FG) = (a)/(FG) Rearrange the equation to solve for FG: FG = (a)/(()) The length of side FG is (a)/(()) Step 3: Express side EG using the sine ratio. The sine of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the hypotenuse. () = oppositehypotenuse Substitute the known values: () = (EF)/(EG) = (a)/(EG) Rearrange the equation to solve for EG: EG = (a)/(()) The length of side EG is (a)/(()) Send me the next one 📸