A vertical pole 6 m tall casts a shadow 4 m long on level ground…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A vertical pole m tall casts a shadow m long on level ground. At the same moment, a tree casts a shadow m long. How tall is the tree?
Need a reminder? The key ideaShow
Two triangles are similar if two angles of one equal two angles of the other (AA). They are also similar if their three side ratios are equal (SSS), or if one angle is equal and the sides around it are in the same ratio (SAS). Write similar triangles with their letters in matching order, and match the sides in that order: .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The triangles. The pole and the tree are upright, and the sun's rays meet the ground at the same angle. Two angles match, so the two triangles are similar by AA.
Step 2. The ratio. .
Step 3. Solve. .
Answer: the tree is m tall.
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