A tree cast a 32.5-foot-long shadow at the same time a 24 foot flagpole cast a 15 foot-long shadow. Find the height of the tree

Question

A tree cast a 32.5-foot-long shadow at the same time a 24 foot flagpole cast a 15 foot-long shadow. Find the height of the tree

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Mary 2 weeks 2021-10-04T15:50:02+00:00 1 Answer 0

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    2021-10-04T15:51:12+00:00

    The height of tree is 52 feet

    Solution:

    Given that,

    Let, Height of tree = x

    shadow of tree = 32.5 feet

    height of flagpole = 24 foot

    shadow of flagpole = 15 foot

    Set up a proportion comparing the height of each object to the length of the shadow

    Therefore,

    \frac{ \text{ Height of tree }}{ \text{ shadow of tree }} = \frac{ \text{height of flagpole }}{ \text{ shadow of flagpole} }

    Substituting the values we get,

    \frac{x}{32.5} = \frac{24}{15}\\\\15x = 24 \times 32.5\\\\15x = 780\\\\x = 52

    Thus height of tree is 52 feet

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