Question

at a certain time of day, the sun shines on a large flagpole causing a shadow that is as long as the flagpole is tall. what is the height of the flagpole to the nearest tenth of a foot?
the height of the flagpole is □ ft.
(round to the nearest tenth as needed.)
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Explanation:

Step1: Define variables and relationship

Let \( h \) = height of flagpole, \( l \) = length of shadow. Given \( l = h \). The hypotenuse (distance from top of pole to end of shadow) is 30 ft.

Step2: Apply Pythagorean theorem

For right triangle: \( h^2 + l^2 = 30^2 \). Substitute \( l=h \):
$$h^2 + h^2 = 900$$

Step3: Simplify and solve for \( h \)

Combine terms: \( 2h^2 = 900 \)
Divide by 2: \( h^2 = 450 \)
Take square root: \( h = \sqrt{450} = \sqrt{225 \times 2} = 15\sqrt{2} \)

Step4: Calculate decimal value

\( 15\sqrt{2} \approx 15 \times 1.4142 = 21.213 \)
Round to nearest tenth: \( h \approx 21.2 \)

Answer:

21.2 ft