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Answer :
Final answer:
To find the angle of elevation, we can use the concept of similar triangles. The angle of elevation from the tip of the shadow to the top of Rusty's head is approximately 39.4º (option c).
Explanation:
To find the angle of elevation from the tip of the shadow to the top of Rusty's head, we can use the concept of similar triangles. Let's represent Rusty's height as h and the length of his shadow as s. Since the triangles formed by the height and shadow and the height and the line connecting the top of the shadow to the top of Rusty's head are similar, we can set up the following proportion:
h/7 = 5.75/s
Cross-multiplying and solving for h, we have:
h = (5.75 * 7)/s
The angle of elevation can be found using the inverse tangent function:
angle = atan(h/s)
Plugging in the values, we have:
angle = atan((5.75 * 7)/s)
Rounding the answer to the nearest tenth, the angle of elevation from the tip of the shadow to the top of Rusty's head is approximately 39.4º (option c).
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