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
Step 1: Define variables and set up the trigonometric relationships. Let h_1 be the height of the first building, h_1 = 66 m. Let h_2 be the height of the taller building. Let x be the horizontal distance between the two buildings. From the top of the first building, the angle of depression to the foot of the taller building is 51^. This forms a right-angled triangle where the opposite side is h_1 and the adjacent side is x. (51^) = (h_1)/(x) From the top of the first building, the angle of elevation to the top of the taller building is 34^. This forms another right-angled triangle where the opposite side is h_2 - h_1 and the adjacent side is x. (34^) = (h_2 - h_1)/(x) Step 2: Calculate the horizontal distance x using the angle of depression. Substitute h_1 = 66 m into the first equation: (51^) = (66)/(x) Solve for x: x = (66)/((51^)) x ≈ (66)/(1.2349) x ≈ 53.445 m Step 3: Calculate the additional height of the taller building using the angle of elevation. Let h_add = h_2 - h_1. Substitute this into the second equation: (34^) = h_addx Solve for h_add: h_add = x (34^) Substitute the value of x from Step 2: h_add ≈ 53.445 m × (34^) h_add ≈ 53.445 m × 0.6745 h_add ≈ 36.04 m Step 4: Calculate the total height of the taller building. The total height of the taller building h_2 is the sum of the height of the first building h_1 and the additional height h_add. h_2 = h_1 + h_add h_2 = 66 m + 36.04 m h_2 = 102.04 m Rounding to one decimal place: h_2 ≈ 102.0 m The height of the taller building is 102.0 m. 3 done, 2 left today. You're making progress.