Shadow Problem?
A vertical pole of height 6 meters casts a shadow of 4 meters. At the same time, a tower of unknown height casts a shadow of 8 meters. How tall is the tower, assuming the angle of elevation of the sun remains the same?
1 Answer
📌 CONCEPT: The shadow problem is an application of similar triangles to find the height of an object, given the lengths of its shadow and the known height of another object and its shadow under the same angle of elevation.
📐 RULE / FORMULA: We use the proportion of the heights of the objects to the lengths of their shadows, which is a direct proportionality, to find the unknown height.
💡 WORKED EXAMPLE: Suppose a vertical pole of height 5 meters casts a shadow of 3 meters. At the same time, a tower of unknown height casts a shadow of 6 meters. We can use the proportion: 5/3 = h/6, where h is the unknown height of the tower. Solving for h, we get h = (5 × 6) / 3 = 10 meters.
⚠️ COMMON MISTAKE: Students may forget to use the correct proportion or make a mistake in the calculation, leading to an incorrect solution.
17 Aug 26
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