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: Draw a diagram and define variables. Let H be the height of the tower, H = 100 m. Let A be Anna's position and B be Bertha's position. Let F be the base of the tower. The angle of elevation from Anna to the top of the tower is _A = 22^. The angle of elevation from Bertha to the top of the tower is _B = 18^. Since the girls are on opposite sides of the tower, the total distance between them is the sum of their distances from the base of the tower. Let d_A be the distance from Anna to the base of the tower (AF) and d_B be the distance from Bertha to the base of the tower (FB). Step 2: Calculate the distance from Anna to the base of the tower (d_A). In the right-angled triangle formed by Anna, the base of the tower, and the top of the tower: (_A) = (H)/(d_A) (22^) = (100)/(d_A) d_A = (100)/((22^)) d_A ≈ (100)/(0.404026) d_A ≈ 247.509 m Step 3: Calculate the distance from Bertha to the base of the tower (d_B). In the right-angled triangle formed by Bertha, the base of the tower, and the top of the tower: (_B) = (H)/(d_B) (18^) = (100)/(d_B) d_B = (100)/((18^)) d_B ≈ (100)/(0.324919) d_B ≈ 307.769 m Step 4: Calculate the total distance between the girls. The total distance D is the sum of d_A and d_B: D = d_A + d_B D ≈ 247.509 m + 307.769 m D ≈ 555.278 m Step 5: Round the answer to the nearest whole number. D ≈ 555 m The distance between the girls is approximately 555 m. Send me the next one 📸