If the length of the shadow on the ground of a pole is 3 times the height of the pole, then the angle of elevation of the Sun is :
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Step-by-Step Solution
Step 1: Define variables and set up the problem
Let h represent the height of the pole and s represent the length of its shadow on the ground. According to the problem statement, the length of the shadow is 3 times the height of the pole, which can be written as s=3h.
Step 2: Formulate the trigonometric relationship
The pole, its shadow, and the line of sight from the top of the pole to the end of the shadow form a right-angled triangle. The angle of elevation, θ, is the angle between the ground (shadow) and the line of sight. In this triangle, the height of the pole (h) is the side opposite to θ, and the length of the shadow (s) is the side adjacent to θ. Therefore, we can use the tangent function.
Step 3: Substitute the given relationship into the tangent equation
Now, substitute the given relationship s=3h into the tangent equation. This will allow us to simplify the expression and find the value of tanθ.
Step 4: Simplify and find the angle of elevation
After substituting, the h terms cancel out, leaving tanθ=31. We know that the angle whose tangent is 31 is 30∘. Therefore, the angle of elevation of the Sun is 30∘.