Practice Indirect Measurement in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Indirect measurement finds unknown lengths by using proportional relationships instead of direct measuring tools.
Use a smaller, measurable shadow to infer a taller object’s height.
Example 1
mediumA tree casts a shadow of 15 m at the same time a 2 m pole casts a shadow of 3 m. How tall is the tree?
Example 2
hardFrom a point 60 m from the base of a building, the angle of elevation to the top is 50°. Find the height of the building to the nearest metre.
Example 3
easyA 6-foot person casts a 4-foot shadow. At the same time, a nearby flagpole casts a 20-foot shadow. How tall is the flagpole?
Example 4
mediumTo measure river width, a surveyor marks A and B on one bank with AB = 80 m. A tree T on the other bank is directly opposite A (so \angle TAB = 90°). From B, the angle \angle TBA = 52°. Find width AT.