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, Ntombenhle.💋 Let's tackle all these questions from the diagram. 1.1.1 Write down the length of FG in terms of a and . Step 1: Identify the trigonometric ratio relating the opposite side (EF = a), the adjacent side (FG), and the angle (). The tangent function relates the opposite and adjacent sides. () = oppositeadjacent = (EF)/(FG) Step 2: Substitute the given values and solve for FG. () = (a)/(FG) FG = (a)/(()) The length of FG is (a)/(()) 1.1.2 Write down the length of EG in terms of a and . Step 1: Identify the trigonometric ratio relating the opposite side (EF = a), the hypotenuse (EG), and the angle (). The sine function relates the opposite side and the hypotenuse. () = oppositehypotenuse = (EF)/(EG) Step 2: Substitute the given values and solve for EG. () = (a)/(EG) EG = (a)/(()) The length of EG is (a)/(()) 1.1.3 If a = 12 and = 35^, calculate the length of FG. Step 1: Use the formula for FG derived in 1.1.1. FG = (a)/(()) Step 2: Substitute a = 12 and = 35^ and calculate. FG = (12)/((35^)) FG ≈ (12)/(0.7002075) FG ≈ 17.138 The length of FG is 17.14 (rounded to two decimal places). 1.1.4 If a = 12 and = 35^, calculate the length of EG. Step 1: Use the formula for EG derived in 1.1.2. EG = (a)/(()) Step 2: Substitute a = 12 and = 35^ and calculate. EG = (12)/((35^)) EG ≈ (12)/(0.5735764) EG ≈ 20.920 The length of EG is 20.92 (rounded to two decimal places). 1.1.5 If FG = 20 and = 40^, calculate the length of EF. Step 1: Use the tangent ratio: () = (EF)/(FG). Step 2: Substitute FG = 20 and = 40^ and solve for EF. (40^) = (EF)/(20) EF = 20 × (40^) EF ≈ 20 × 0.8390996 EF ≈ 16.781 The length of EF is 16.78 (rounded to two decimal places). 1.1.6 If EG = 30 and = 50^, calculate the length of EF. Step 1: Use the sine ratio: () = (EF)/(EG). Step 2: Substitute EG = 30 and = 50^ and solve for EF. (50^) = (EF)/(30) EF = 30 × (50^) EF ≈ 30 × 0.7660444 EF ≈ 22.981 The length of EF is 22.98 (rounded to two decimal places). 3 done, 2 left today. You're making progress.