Questions: Question A tree casts a 38 foot shadow at the same time a boy casts a 9 foot shadow. If the boy is 5.5 feet tall, how tall is the tree? Round to the nearest tenth of a foot.

Question
A tree casts a 38 foot shadow at the same time a boy casts a 9 foot shadow. If the boy is 5.5 feet tall, how tall is the tree? Round to the nearest tenth of a foot.

Transcript text: Question A tree casts a 38 foot shadow at the same time a boy casts a 9 foot shadow. If the boy is 5.5 feet tall, how tall is the tree? Round to the nearest tenth of a foot.

Solution

Solution Steps

Step 1: Establish the Proportionality

Given that the ratio of the height of an object to the length of its shadow is constant, we can establish the following proportionality: $$\frac{h_A}{s_A} = \frac{h_B}{s_B}$$ where:

$h_A$ is the height of Object A, which is 5.5 units.
$s_A$ is the shadow length of Object A, which is 9 units.
$s_B$ is the shadow length of Object B, which is 38 units.
$h_B$ is the height of Object B, which we want to find.

Step 2: Solve for the Unknown Height

Rearranging the equation to solve for $h_B$, we get: $$h_B = \frac{h_A \times s_B}{s_A}$$ Substituting the known values into the equation: $$h_B = rac{5.5 imes 38}{9}$$ $$h_B = 23.2$$ (rounded to 1 decimal places)

Final Answer:

The height of Object B is approximately 23.2 units.

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