Question

at a certain time of day, the sun shines on a large flagpole causing a shadow that is twice 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 )

Explanation:

Step1: Define variables

Let $h$ = height of flagpole (ft). Shadow length = $2h$ (ft).

Step2: Apply Pythagorean theorem

The flagpole, shadow, and sun's ray form a right triangle.
$$h^2 + (2h)^2 = 300^2$$

Step3: Simplify the equation

$$h^2 + 4h^2 = 90000$$
$$5h^2 = 90000$$

Step4: Solve for $h^2$

$$h^2 = \frac{90000}{5} = 18000$$

Step5: Calculate $h$

$$h = \sqrt{18000} \approx 134.16$$

Step6: Round to nearest tenth

Round 134.16 to 134.2.

Answer:

134.2 ft