Question

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You measure a tree's shadow and find that it is x = 11 meters long. Then you measure the shadow of a nearby two-meter lamppost and find that is 75 centimeters long.

How tall (in m) is the tree? (Round your answer to one decimal place.)

Answer 1

29.3 m (1 d.p.)

Explanation:

The given scenario can be modelled as two similar right triangles:

Triangle 1

• Base = x = 11 m
• Height = h

Triangle 2

• Base = 0.75 m
• Height = 2 m

In similar triangles, corresponding sides are always in the same ratio.

Therefore:

`\implies \sf base\; 1 : base\; 2 = height\; 1 : height\; 2`

`\implies \sf 11 : 0.75 = h : 2`

`\implies \sf (11)/(0.75) = (h)/(2)`

`\implies \sf 2 \cdot 11 = 0.75 \cdot h`

`\implies \sf 22 = 0.75h`

`\implies \sf h = 29.3 \;m\;\; (1 d.p.)`

Answer 2

• 29.3 m

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The shadows and heights represent corresponding sides of similar triangles.

To find the height use ratios:

• h / 2 = 11/0.75
• h = 2*11/0.75
• h = 29.3 m (rounded)