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Rusty is 5.75 feet tall and casts a 7-foot shadow. Find the angle of elevation from the tip of the shadow to the top of Rusty’s head. Round your answer to the nearest tenth.

A. 50.6º
B. 9.1º
C. 39.4º
D. 55.2º

Answer :

Final answer:

The angle of elevation from the tip of Rusty's shadow to the top of Rusty's head can be calculated using the tangent function of trigonometry. The result is approximately 39.4º.

Explanation:

To find the angle of elevation from the tip of Rusty's shadow to the top of Rusty's head, we would have to use trigonometry, specifically, the tangent function (Tan). By definition, Tangent of an angle in a right triangle is the ratio of the side opposite the angle to the side adjacent to the angle.

Let's call the angle of elevation θ. The side opposite to θ is Rusty's height, which is 5.75 feet, and the side adjacent to θ is the length of the shadow, which is 7 feet. Thus, Tan θ = 5.75/7.

To find the angle θ, we now take the inverse tangent of (5.75/7). This can usually be found on a scientific calculator with the 'Tan^-1' button.

Doing the above calculation, θ = Tan^-1(5.75/7), we find that the angle of elevation to the nearest tenth to be 39.4º.

So, the answer is (c) 39.4º.

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