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You are standing 42 feet away from the base of the Statue of Liberty looking up at an angle of
82.2^(@). How tall is the statue?

You are standing $42$ feet away from the base of the Statue of Liberty looking up at an angle of $82.2^\circ$ . How tall is the statue?

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Pythagorean theorem

Full solution

Q. You are standing

42

feet away from the base of the Statue of Liberty looking up at an angle of

82.2^\circ

. How tall is the statue?

Identify Relationship: Identify the relationship between the angle, adjacent side, and opposite side in a right triangle. $\newline$ Using the tangent function, $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$ . $\newline$ Here, $\theta = 82.2$ degrees, $\text{adjacent} = 42$ feet.
Calculate Height: Calculate the height of the Statue of Liberty using the tangent function. $\newline$ $\tan(82.2) = \frac{\text{height}}{42}$ $\newline$ $\text{height} = 42 \times \tan(82.2)$
Use Calculator: Use a calculator to find $\tan(82.2 \text{ degrees})$ . $\tan(82.2) \approx 7.115$ $\text{height} = 42 \times 7.115$
Perform Multiplication: Perform the multiplication to find the height. $\newline$ $\text{height} = 42 \times 7.115 = 298.83$ feet

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