Question : Subhas, a 3.15 m tall tree, and an 11.25 m tall building are positioned such that their feet on the ground are collinear and the tree is located between Subhas and the building. The tree is located at a distance of 7.5 m from Subhas and a distance of 45 m from the building. Further, the eyes of Subhas, the top of the tree, and the top of the building fall in one line. Find the height (in m ) from the ground at which Subhas's eyes are situated.
Option 1: 1.75
Option 2: 1.8
Option 3: 1.6
Option 4: 1.5
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Correct Answer: 1.8
Solution : Let XA be Subhas, YB be the tree, and ZC be the building. YB = 3.15 m ZC = 11.25 m AB = 7.5 m BC = 45 m XO = AB = 7.5 m OP = BC = 45 m ⇒ XP = XO + OP = 7.5 + 45 = 52.5 m Let the height from the ground at which Subhas's eyes are situated be $h$. OY = BY – OB = 3.15 – $h$ PZ = ZC – PC = 11.25 – $h$ Let the angle of elevation be $\theta$. In $\triangle$XPZ, $\tan \theta = \frac{\text{PZ}}{\text{PX}} = \frac{11.25-h}{52.5}$ -----------(i) In $\triangle$XOY, $\tan \theta = \frac{\text{OY}}{\text{OX}} = \frac{3.15-h}{7.5}$ ------------(ii) $⇒ \frac{11.25-h}{52.5} = \frac{3.15-h}{7.5}$ $⇒ \frac{11.25-h}{7} = \frac{3.15-h}{1}$ $⇒11.25-h = 7(3.15-h)$ $⇒11.25-h = 22.05-7h$ $⇒6h = 10.8$ $\therefore h = \frac{10.8}{6} = 1.8$ m Hence, the correct answer is 1.8.
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Question : Suhas, a 3.15 m tall tree, and an 11.25 m tall building are positioned such that their feet on the ground are collinear and the tree is located between Suhas and the building. The tree is located at a distance of 45 m from the building. Further. the eyes of Suhas, the top of the tree, and the top of the building fall in one line, and the eyes of Suhas are at a height of 1.8 m from the ground, At what distance (in m) from Suhas is the tree located?
Option 1: 6
Option 2: 5
Option 3: 7.5
Option 4: 9
Question : Suhas, a 3.15 m tall tree, and a building are positioned such that their feet on the ground are collinear and the tree is located between Suhas and the building. The tree is located at a distance of 7.5 m from Suhas and a distance of 45 m from the building. Further, the eyes of Suhas, the top of the tree, and the top of the building fall in one line, and the eyes of Suhas are at a height of 1.8 m from the ground. Find the height (in m) of the building.
Option 1: 11.25
Option 2: 11.50
Option 3: 10.25
Option 4: 10.75
Question : Suhas, a tree, and an 11.25 m tall building are positioned such that their feet on the ground are collinear and the tree is located between Suhas and the building. The tree is located at a distance of 7.5 m from Suhas and a distance of 45 m from the building. Further, the eyes of Suhas, the top of the tree, and the top of the building fall in one line, and the eyes of Suhas are at a height of 1.8 m from the ground. Find the height (in m ) of the tree.
Option 1: 3.00 m
Option 2: 3.30 m
Option 3: 3.15 m
Option 4: 3.45 m
Question : From two points on the ground lying in a straight line through the foot of a pillar, the two angles of elevation of the top of the pillar are complementary to each other. If the distance of the two points from the foot of the pillar are 9 m and 16 m and the two points lie on the same side of the pillar, then the height of the pillar is:
Option 1: 5 m
Option 2: 10 m
Option 3: 7 m
Option 4: 12 m
Question : A vertical pole and vertical tower are standing on the same level of ground. The height of the pole is 10 m. From the top of the pole, the angle of elevation of the top of the tower and the angle of depression of the foot of the tower are 60° and 30° respectively. The height of the tower is:
Option 1: 20 m
Option 2: 30 m
Option 3: 40 m
Option 4: 50 m
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