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
Hey ireenkiriungi24, good to see you again. 39. a) Calculate the length of BC Step 1: Use the Pythagorean theorem for the right-angled triangle ABC. AC^2 = AB^2 + BC^2 Step 2: Substitute the given values. (85 cm)^2 = (13 cm)^2 + BC^2 7225 cm^2 = 169 cm^2 + BC^2 Step 3: Solve for BC^2. BC^2 = 7225 cm^2 - 169 cm^2 BC^2 = 7056 cm^2 Step 4: Calculate BC. BC = sqrt(7056 cm)^2 BC = 84 cm The length of BC is 84 cm. b) The value of angle BAC in degrees, correct to 2 decimal places using tangent tables only. Step 1: Identify the sides relative to angle BAC (). Opposite side = BC = 84 cm Adjacent side = AB = 13 cm Step 2: Use the tangent ratio. () = OppositeAdjacent = (BC)/(AB) () = (84)/(13) () ≈ 6.461538 Step 3: Find the angle . = (6.461538) Using a calculator (as an AI, I don't have physical tangent tables to interpolate from), ≈ 81.2009^ Step 4: Round to 2 decimal places. ≈ 81.20^ The value of angle BAC is 81.20^. 40. Determine the value of x. Step 1: Use the trigonometric identity () = (90^ - ). Given (3x^) = ((x-60)^). We can rewrite (3x^) as (90^ - 3x^). So, the equation becomes: (90^ - 3x^) = ((x-60)^) Step 2: Equate the angles, since x is an acute angle, 3x and x-60 will be in ranges where this direct equality holds. 90 - 3x = x - 60 Step 3: Solve for x. 90 + 60 = x + 3x 150 = 4x x = (150)/(4) x = 37.5 The value of x is 37.5. 41. a) Calculate the amount of money in Ksh, that she obtained after exchanging the foreign currencies. Step 1: Determine the exchange rate to use. Since the businesswoman arrived in Kenya with foreign currency, she is selling it to the bank. The bank will buy her currency. Buying rate for 1 Euro = 125 Ksh Buying rate for 1 Sterling Pound = 152 Ksh Step 2: Calculate the amount from Sterling Pounds. 1580 Sterling Pounds × 152 Ksh/Sterling Pound = 239960 Ksh Step 3: Calculate the amount from Euros. 1205 Euros × 125 Ksh/Euro = 150625 Ksh Step 4: Calculate the total amount obtained. 239960 Ksh + 150625 Ksh = 390585 Ksh The businesswoman obtained 390585 Ksh. b) Calculate the amount of money, in Ksh that she needed for the exchange. Step 1: Determine the exchange rate to use. Since the trader is travelling abroad and needs foreign currency, she is buying it from the bank. The bank will sell her the currency. Selling rate for 1 Euro = 128 Ksh Selling rate for 1 Sterling Pound = 158 Ksh Step 2: Calculate the cost for Euros. 1250 Euros × 128 Ksh/Euro = 160000 Ksh Step 3: Calculate the cost for Sterling Pounds. 1520 Sterling Pounds × 158 Ksh/Sterling Pound = 240160 Ksh Step 4: Calculate the total amount needed. 160000 Ksh + 240160 Ksh = 400160 Ksh The trader needed 400160 Ksh for the exchange. Send me the next one 📸