A building is 24m away from a mast. The angle of depression to the foot of the mast is 45 degrees. The angle of elevation to the top of the mast is 60 degrees. Calculate the height of the mast.

Welcome back adejinledemolae — missed you this week. Here are the solutions to your assignment questions: Problem 1: Let H be the height of the building, h be the height of the mast, and x be the distance between the building and the mast. We are given x = 24 m. Let h_1 be the part of the mast above the height of the building. The angle of depression to the foot of the mast is 45^. The angle of elevation to the top of the mast is 60^. a) Calculate the height of the mast. Step 1: Calculate the height of the building (H). Using the angle of depression to the foot of the mast: (45^) = (H)/(x) H = x (45^) H = 24 × 1 H = 24 m Step 2: Calculate the height of the mast above the building (h_1). Using the angle of elevation to the top of the mast: (60^) = (h_1)/(x) h_1 = x (60^) h_1 = 24 × sqrt(3) h_1 ≈ 24 × 1.73205 h_1 ≈ 41.5692 m Step 3: Calculate the total height of the mast (h). The total height of the mast is the sum of the building's height and the mast's height above the building. h = H + h_1 h = 24 + 24sqrt(3) h = 24(1 + sqrt(3)) h ≈ 24(1 + 1.73205) h ≈ 24(2.73205) h ≈ 65.5692 m Rounding to two decimal places: 65.57 m b) Calculate the distance between the top of the building and the top of the mast. Step 1: Use trigonometry to find the distance (D). This distance is the hypotenuse of the right-angled triangle formed by the horizontal distance (x) and the height h_1. (60^) = (x)/(D) D = (x)/((60^)) D = (24)/(0.5) D = 48 m 48 m Problem 2: Let x be the distance from point H to the foot of the tower, x = 20 m. Let h_T be the height of the tower. Let h_C be the total height from the ground to the top of the mast. The angle of elevation to the top of the tower (T) is 30^. The angle of elevation to the top of the mast (C) is 50^. We need to correct all answers to the nearest whole number. a) Calculate the height of the tower. Step 1: Calculate the height of the tower (h_T). Using the angle of elevation to the top of the tower: (30^) = (h_T)/(x) h_T = x (30^) h_T = 20 × (1)/(sqrt(3)) h_T = 20sqrt(3)3 h_T ≈ (20 × 1.73205)/(3) h_T ≈ 11.547 m Rounding to the nearest whole number: 12 m b) Calculate the height of the mast. Step 1: Calculate the total height to the top of the mast (h_C). Using the angle of elevation to the top of the mast: (50^) = (h_C)/(x) h_C = x (50^) h_C = 20 (50^) h_C ≈ 20 × 1.19175 h_C ≈ 23.835 m Rounding to the nearest whole number: h_C ≈ 24 m Step 2: Calculate the height of the mast (h_M). The height of the mast is the difference between the total height to the top of the mast and the height of the tower. h_M = h_C - h_T h_M ≈ 23.835 - 11.547 h_M ≈ 12.288 m Rounding to the nearest whole number: 12 m Send me the next one 📸