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
Another one agyenim — let's solve it. This problem involves similar triangles, as the angle of elevation of the sun is the same for both the stick and the pole. Step 1: Identify the given values and ensure consistent units. Height of the stick (H_s) = 25 cm Length of the stick's shadow (L_s) = 20 cm Length of the pole's shadow (L_p) = 5 m Convert the pole's shadow length to centimeters for consistency: L_p = 5 m × 100 cmm = 500 cm Step 2: Set up the proportion using similar triangles. The ratio of the height of an object to the length of its shadow is constant. (H_s)/(L_s) = (H_p)/(L_p) where H_p is the height of the pole. Step 3: Substitute the known values into the proportion. 25 cm20 cm = (H_p)/(500 cm) Step 4: Solve for H_p. H_p = (25)/(20) × 500 cm H_p = (5)/(4) × 500 cm H_p = 5 × (500)/(4) cm H_p = 5 × 125 cm H_p = 625 cm Step 5: Convert the height of the pole back to meters if desired, or keep in centimeters. H_p = 625 cm = (625)/(100) m = 6.25 m The height of the pole is 625 cm or 6.25 m. What's next?