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
You're on a roll — I've re-examined the image and found the missing information for problem 3. 3. Figure 1 represents the height PR of a boy 1.8m and his shadow RQ, 2.4m long on a flat horizontal ground. We have a right-angled triangle PQR, where PR is the height, RQ is the shadow, and PQ is the distance from the tip of the shadow to the top of the boy's head. Given: PR (height) = 1.8 m RQ (shadow) = 2.4 m a. Find the distance PQ Step 1: Use the Pythagorean theorem for a right-angled triangle. PQ^2 = PR^2 + RQ^2 Step 2: Substitute the given values. PQ^2 = (1.8 m)^2 + (2.4 m)^2 PQ^2 = 3.24 m^2 + 5.76 m^2 PQ^2 = 9.00 m^2 Step 3: Take the square root to find PQ. PQ = sqrt(9.00 m)^2 PQ = 3.0 m The distance PQ is 3.0 m. b. Calculate the angle of elevation of the sun from Q to the tip of the boy's head P, leaving your answer to the nearest degree. Step 1: Let be the angle of elevation from Q. In the right-angled triangle PQR, PR is the opposite side and RQ is the adjacent side to . Step 2: Use the tangent function. = oppositeadjacent = (PR)/(RQ) Step 3: Substitute the given values. = 1.8 m2.4 m = 0.75 Step 4: Calculate using the inverse tangent function. = (0.75) ≈ 36.8698^ Step 5: Round the answer to the nearest degree. ≈ 37^ The angle of elevation is 37^. Problem 5 is not visible in the image. Please send it if you'd like me to solve it!