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
Here's how to solve the problem: Let's denote the position of Zama at the top of the building as A, the base of the building as B, and Peter's position on the ground as C. This forms a right-angled triangle ABC, with the right angle at B. The height of the building (AB) is 13 m. The angle of declination from Zama to Peter is 30^. This means the angle of elevation from Peter to Zama ( ACB) is also 30^ (alternate interior angles). a) Calculate the distance between Zama and Peter. Step 1: Identify the known values and the unknown. We know the opposite side (height of the building, AB = 13 m) and the angle ( ACB = 30^). We need to find the hypotenuse (distance between Zama and Peter, AC). Step 2: Use the sine trigonometric ratio. () = oppositehypotenuse (30^) = (AB)/(AC) (30^) = (13)/(AC) Step 3: Solve for AC. AC = (13)/((30^)) Since (30^) = 0.5: AC = (13)/(0.5) AC = 26 m The distance between Zama and Peter is 26 m. b) How far is Peter from the building? Step 4: Identify the known values and the unknown. We know the opposite side (height of the building, AB = 13 m) and the angle ( ACB = 30^). We need to find the adjacent side (distance Peter is from the building, BC). Step 5: Use the tangent trigonometric ratio. () = oppositeadjacent (30^) = (AB)/(BC) (30^) = (13)/(BC) Step 6: Solve for BC. BC = (13)/((30^)) Since (30^) = (1)/(sqrt(3)): BC = (13)/(1/sqrt(3)) BC = 13sqrt(3) m BC ≈ 13 × 1.73205 BC ≈ 22.5 m Peter is approximately 22.5 m from the building. Send me the next one 📸