When a tree's shadow length is √3 times its height, what is the sun's elevation angle:________?
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Answer: A. 30°
Explanation
The tangent of the elevation angle is calculated as tree height divided by shadow length. Substituting the given ratio yields one divided by the square root of three. Trigonometric tables confirm that the angle whose tangent equals this value is thirty degrees. Right angled triangles relate acute angles to the ratios of their opposite and adjacent sides. The tangent function specifically represents the ratio of the opposite side to the adjacent side. Standard trigonometric values show that tangent of thirty degrees equals one over square root three.
Surveyors use similar trigonometric principles to measure heights of tall structures without direct climbing. Shadow measurements combined with solar angles help determine building heights and spacing requirements. Navigation and astronomy rely heavily on right triangle relationships to calculate unknown distances accurately. Option B suggests forty five degrees which corresponds to equal height and shadow lengths. Option C suggests sixty degrees which occurs when shadow length equals height divided by root three. Option D suggests ninety degrees which represents a vertical sun position with zero shadow.
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- Mathematics
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- Mathematics
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