If the angle of elevation of the sun is 42°, which of the following equations solves for the length of the shadow on the level ground of a man who is 6.1 ft tall? Let x, in ft, be such length.
Question
If the angle of elevation of the sun is 42°, which of the following equations solves for the length of the shadow on the level ground of a man who is 6.1 ft tall? Let x, in ft, be such length.
Solution
The problem involves a right triangle, where the man is one side of the triangle, the shadow is the other side, and the angle of elevation is the angle between the ground and the line from the man to the sun.
In trigonometry, the tangent of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
So, we can set up the following equation using the tangent of the angle of elevation (42°), the height of the man (6.1 ft), and the length of the shadow (x ft):
tan(42°) = 6.1 / x
To solve for x, we can rearrange the equation:
x = 6.1 / tan(42°)
This equation will give the length of the shadow.
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