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.
211)
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
