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1. A man observes, that when he moves up a distance c meters on a slope, the angle of depression of a
point on the horizontal plane from the base of the slope is 30º; and when he moves up further a distance
c meters the angle of depression of that point is 45º. Obtain the angle of elevation of the slope with the
horizontal.
2. A vertical pole (more than 100 ft high) consists of two portions, the lower being one third of the whole. If the
upper portion subtends an angle tan–1 (1/2) at a point in the horizontal plane through the foot of the pole
and at a distance of 40ft from it, find the height of the pole.
3. A man standing south of a lamp-post observes his shadow on the horizontal plane to be 24 feet long. On
walking eastward a distance of 300 feet, he finds that his shadow is now 30 feet. If his height is 6ft, find the
height of the lamp above the horizontal plane.
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4 Answers
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Let the point A be observed from Q and R
⇒ PQ = QR = c
Apply m – n theorem in ΔAPR. Q divides PR in ratio c : c
⇒ (c + c) cot (θ – 30º) = c cot 15º – c cot 30º
⇒ (c + c) cot (θ – 30º) = c cot 15º – c cot 30º
⇒ 2 cot (θ – 30º) = 2 +√ 3 − √3
⇒ 2 cot (θ – 30º) = 2
⇒ cot (θ – 30º) = 1
⇒ θ – 30º = 45º
⇒ θ = 75º