a) Calculate the length of BC. b) Calculate the value of angle BAC in degrees, correct to 2 decimal places using tangent tables only. 40. Determine the value of x.

Question

Asked on April 12, 2026Mathematics

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.

Accepted Answer · 2026-04-12T08:04:16.802Z

Morning — let's get this done. 39. a) Calculate the length of BC Step 1: Use the Pythagorean theorem for the right-angled triangle ABC, where B is the right angle. AB^2 + BC^2 = AC^2 Step 2: Substitute the given values AB = 13 cm and AC = 85 cm. 13^2 + BC^2 = 85^2 169 + BC^2 = 7225 Step 3: Solve for BC^2. BC^2 = 7225 - 169 BC^2 = 7056 Step 4: Calculate BC. BC = sqrt(7056) BC = 84 cm The length of BC is 84 cm. b) Calculate the value of angle BAC in degrees, correct to 2 decimal places using tangent tables only. Step 1: Identify the tangent ratio for angle BAC. ( BAC) = OppositeAdjacent = (BC)/(AB) Step 2: Substitute the values of BC and AB. ( BAC) = (84)/(13) ( BAC) ≈ 6.461538 Step 3: Find the angle whose tangent is approximately 6.461538. BAC = (6.461538) BAC ≈ 81.2006^ Step 4: Round to 2 decimal places. BAC ≈ 81.20^ The value of angle BAC is 81.20^. 40. Determine the value of x. Step 1: Use the complementary angle 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 the sine values are equal and x is acute. 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: Calculate the Ksh obtained from Sterling Pounds. The bank buys foreign currency. Ksh from Sterling Pounds = 1580 Sterling Pounds × 152 Ksh/Sterling Pound Ksh from Sterling Pounds = 239920 Ksh Step 2: Calculate the Ksh obtained from Euros. The bank buys foreign currency. Ksh from Euros = 1205 Euros × 125 Ksh/Euro Ksh from Euros = 150625 Ksh Step 3: Calculate the total amount in Ksh. Total Ksh = 239920 Ksh + 150625 Ksh Total Ksh = 390545 Ksh The businesswoman obtained 390545 Ksh. b) Calculate the amount of money, in Ksh that she needed for the exchange. Step 1: Calculate the Ksh needed to buy Euros. The bank sells foreign currency. Ksh for Euros = 1250 Euros × 128 Ksh/Euro Ksh for Euros = 160000 Ksh Step 2: Calculate the Ksh needed to buy Sterling Pounds. The bank sells foreign currency. Ksh for Sterling Pounds = 1520 Sterling Pounds × 158 Ksh/Sterling Pound Ksh for Sterling Pounds = 240160 Ksh Step 3: Calculate the total amount in Ksh needed. Total Ksh needed = 160000 Ksh + 240160 Ksh Total Ksh needed = 400160 Ksh The trader needed 400160 Ksh. Send me the next one 📸

Accepted Answer · 2026-04-12T08:04:16.802Z

Morning — let's get this done. 39. a) Calculate the length of BC Step 1: Use the Pythagorean theorem for the right-angled triangle ABC, where B is the right angle. AB^2 + BC^2 = AC^2 Step 2: Substitute the given values AB = 13 cm and AC = 85 cm. 13^2 + BC^2 = 85^2 169 + BC^2 = 7225 Step 3: Solve for BC^2. BC^2 = 7225 - 169 BC^2 = 7056 Step 4: Calculate BC. BC = sqrt(7056) BC = 84 cm The length of BC is 84 cm. b) Calculate the value of angle BAC in degrees, correct to 2 decimal places using tangent tables only. Step 1: Identify the tangent ratio for angle BAC. ( BAC) = OppositeAdjacent = (BC)/(AB) Step 2: Substitute the values of BC and AB. ( BAC) = (84)/(13) ( BAC) ≈ 6.461538 Step 3: Find the angle whose tangent is approximately 6.461538. BAC = (6.461538) BAC ≈ 81.2006^ Step 4: Round to 2 decimal places. BAC ≈ 81.20^ The value of angle BAC is 81.20^. 40. Determine the value of x. Step 1: Use the complementary angle 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 the sine values are equal and x is acute. 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: Calculate the Ksh obtained from Sterling Pounds. The bank buys foreign currency. Ksh from Sterling Pounds = 1580 Sterling Pounds × 152 Ksh/Sterling Pound Ksh from Sterling Pounds = 239920 Ksh Step 2: Calculate the Ksh obtained from Euros. The bank buys foreign currency. Ksh from Euros = 1205 Euros × 125 Ksh/Euro Ksh from Euros = 150625 Ksh Step 3: Calculate the total amount in Ksh. Total Ksh = 239920 Ksh + 150625 Ksh Total Ksh = 390545 Ksh The businesswoman obtained 390545 Ksh. b) Calculate the amount of money, in Ksh that she needed for the exchange. Step 1: Calculate the Ksh needed to buy Euros. The bank sells foreign currency. Ksh for Euros = 1250 Euros × 128 Ksh/Euro Ksh for Euros = 160000 Ksh Step 2: Calculate the Ksh needed to buy Sterling Pounds. The bank sells foreign currency. Ksh for Sterling Pounds = 1520 Sterling Pounds × 158 Ksh/Sterling Pound Ksh for Sterling Pounds = 240160 Ksh Step 3: Calculate the total amount in Ksh needed. Total Ksh needed = 160000 Ksh + 240160 Ksh Total Ksh needed = 400160 Ksh The trader needed 400160 Ksh. Send me the next one 📸

a) Calculate the length of BC. b) Calculate the value of angle BAC in degrees, correct to 2 decimal places using tangent tables only. 40. Determine the value of x.

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a) Calculate the length of BC. b) Calculate the value of angle BAC in degrees, correct to 2 decimal places using tangent tables only. 40. Determine the value of x.

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