You have a sundial set up at your location, and you notice that the shadow of the sundial post is 6 feet long at 3:00 PM. Determine the angle between the sundial post and the ground at that time.
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To determine the angle between the sundial post and the ground at 3:00 PM, we can use trigonometry and the concept of similar triangles.
First, let's draw a diagram. Let the length of the sundial post be represented by the letter "h", and the length of the shadow be represented by the letter "s". The angle between the sundial post and the ground can be denoted as θ.
Now, we have a right triangle formed by the sundial post, its shadow, and the ground. The height of the sundial post (h) is the opposite side, the length of the shadow (s) is the adjacent side, and the angle (θ) is the angle between the ground and the hypotenuse.
Using the trigonometric function tangent, we can write the equation:
tan(θ) = opposite/adjacent
tan(θ) = h/s
To find the angle θ, we can take the inverse tangent (arctan) of the ratio of h to s:
θ = arctan(h/s)
Given that the length of the shadow (s) is 6 feet, we need the height of the sundial post (h) to calculate the angle.
Without the height of the sundial post, we cannot determine the angle between the sundial post and the ground at 3:00 PM.
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