Frank stands 500 feet from the base of the Statue of Liberty. If Frank looks up with an angle of elevation of 31', how tall is t he Statue of Liberty, to the nearest foot?
1 answer:
In angles 31' means 31 minutes. And one degree is equal to 60 minutes, then 31' is 31/60 ° = 0.51667 ° That measure is too small if you use it you will obtain this result: x = 500 ft * tan (31/60°) = 4.51 ft which is too little. I will answer the problem using 31° instead of 31'. This is answer and full explanation:Answer: 300 ft. Explanation: You can form a right triangle with these features: 1) Base = adjacent-leg = 500 feet 2) angle between the hypotenuse and the base = 31° 3) Height = opposite-leg = height of the Statue of LIberty = x Now, use the equation for the trigonometric ratio tangent: tan(angle) = opposite-leg / adjacent-leg => tan (31°) = x / 500ft => x = 500ft * tan(31°) x = 300.43 ft which rounded to the nearest foot is 300 ft.
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