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Here is the translation of the above expressions to English: Here is the solution to your question: a) Calculate the height of the tower. Step 1: Identify the given information. We are given the horizontal distance from point P to the tower, d = 100 \, m. The angle of elevation of the top of the tower from P, _e = 15^. The angle of depression of the base of the tower from P, _d = 1^. We need to calculate the height of the tower, h. Step 2: Use trigonometry to represent parts of the tower's height. Let h_1 be the height of the top of the tower above the horizontal line passing through P. Let h_2 be the height of P above the base of the tower. From the angle of elevation: (_e) = (h_1)/(d) h_1 = d (_e) = 100 (15^) From the angle of depression: (_d) = (h_2)/(d) h_2 = d (_d) = 100 (1^) Step 3: Calculate the total height of the tower. The total height of the tower h is the sum of h_1 and h_2. h = h_1 + h_2 = 100 (15^) + 100 (1^) h = 100 ((15^) + (1^)) h = 100 (0.267949 + 0.017455) h = 100 (0.285404) h ≈ 28.54 \, m The height of the tower is 28.54 m. b) i) Calculate the distance from point P to Q. Step 1: Draw a diagram and label the points and angles. Let R be the base of the tower. From P, R is on a bearing of 030^ and a horizontal distance PR = 100 \, m. From Q, R is on a bearing of 330^ and a horizontal distance QR = 70 \, m. Points P and Q are on the same horizontal plane. Step 2: Calculate the interior angle of triangle PQR. The bearing of R from P is 030^. Thus, the angle between the North line from P and PR is 30^. The bearing of R from Q is 330^. Thus, the angle between the North line from Q and QR is 330^. To use the cosine rule, we need the angle PRQ. Bearing of P from R: 030^ + 180^ = 210^. Bearing of Q from R: 330^ - 180^ = 150^. The angle PRQ is the difference between these two bearings. PRQ = 210^ - 150^ = 60^ Step 3: Use the cosine rule to calculate the distance PQ. In triangle PQR, we have PR = 100 \, m, QR = 70 \, m, and PRQ = 60^. The cosine rule states: PQ^2 = PR^2 + QR^2 - 2(PR)(QR)( PRQ) PQ^2 = 100^2 + 70^2 - 2(100)(70)(60^) PQ^2 = 10000 + 4900 - 14000 ((1)/(2)) PQ^2 = 14900 - 7000 PQ^2 = 7900 PQ = sqrt(7900) PQ = sqrt(100 × 79) PQ = 10sqrt(79) PQ ≈ 10 × 8.88819 PQ ≈ 88.88 \, m The distance from P to Q is 88.88 m. That's 2 down. 3 left today — send the next one.