Question

1. a student wants to know how tall the flagpole at her school is, her eye level is 5.5 feet above the ground and she stands 36 feet from the base of the flagpole. if the angle of elevation is 25°, what is the height of the flagpole?

Explanation:

Step1: Define unknown height segment

Let $x$ = vertical height from eye level to flagpole top.

Step2: Use tangent trigonometric ratio

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$, so $\tan(25^\circ) = \frac{x}{36}$

Step3: Solve for $x$

$x = 36 \times \tan(25^\circ)$
Calculate $\tan(25^\circ) \approx 0.4663$, so $x \approx 36 \times 0.4663 = 16.7868$

Step4: Total flagpole height

Add eye level height: $\text{Total Height} = x + 5.5$

Answer:

$\approx 22.3$ feet (rounded to one decimal place; exact calculated value is $\approx 22.2868$ feet)