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To measure the height of a hill, an engineer takes two readings from a clinometer (a device that is used to measure the angle of elevation from the horizontal to an object).

With her first reading, she measured the angle of elevation to the top of the hill to be $46°.$ Her second reading, 400 feet closer to the hill, measures an angle of elevation of $61°.$

If the height of the clinometer is 3 feet, what is the height of the hill?

Note: for any $ {\triangle} $ABC, where $a$ is the side opposite $ \angle $A, where $b$ is the side opposite $ \angle $B, and $c$ is the side opposite $ \angle $C,the Law of Sines states that:

$\cfrac{\sin{A}}{a} = \cfrac{\sin{B}}{b} = \cfrac{\sin{C}}{c}$


$\text{289.7 ft}$


$\text{416.2 ft}$


$\text{723.6 ft}$


$\text{975.3 ft}$


$\text{2007.6 ft}$

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