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Homefsc 1st year math solutionsAngles of Elevation and Depression Exercise 12.3

Angles of Elevation and Depression Exercise 12.3

  1. A vertical pole is 8 \mathrm{~m} high and the length of its shadow is 6 \mathrm{~m}. What is the angle of elevation of the sun at that moment?
  2. A man 18 \mathrm{dm} tall observes that the angle of elevation of the top of a tree at a distance of 12 \mathrm{~m} from him is 32^{\circ}. What is the height of the tree?
  3. At the top of a cliff 80 \mathrm{~m} high, the angle of depression of a boat is 12^{\circ}. How far is the boat from the cliff?
  4. A ladder leaning against a vertical wall makes an angle of 24^{\circ} with the wall. Its foot is 5 \mathrm{~m} from the wall. Find its length.
  5. A kite flying at a height of 67.2 \mathrm{~m} is attached to a fully stretched string inclined at an angle of 55^{\circ} to the horizontal. Find the length of the string.
  6. When the angle between the ground and the suñ is 30^{\circ}, flag pole casts a . shadow of 40 \mathrm{~m} long. Find the height of the top of the flag.
    360 A Texbook of Algebra and Trigononetry
  7. A plane flying directly above a post 6000 \mathrm{~m} away from an anti-aircraft gun observes the gun at an angle of depression of 27^{\circ}. Find the height of the plane.
  1. A man on the top of a 100 \mathrm{~m} high light-house is in line with two ships on the same side of it, whose angles of depression from the man are 17^{\circ} and 19^{\circ} respecting. Find the distance between the ships.
  2. \quad \mathrm{P} and Q are two points in line with a tree. If the distance between P and Q be 30 \mathrm{~m} and the angles of elevation of the top of the tree at P and Q be 12^{\circ} and 15^{\circ} respectively, find the height of the tree.
  3. Two men are on the opposite sides of a 100 \mathrm{~m} high tower. If the measures of the angles of elevation of the top of the tower are 18^{\circ} and 22 respectively find the distance between them.
  4. A man standing 60 \mathrm{~m} away from a tower notices that the angles of elevation of the top and the bottom of a flag staff on the top of the tower are 64^{\circ} and 62^{\circ} respectively. Find the length of the flag staff.
  5. The angle of elevation of the top of a 60 \mathrm{~m} high tower from a point A, on the same level as the foot of the tower, is 25^{\circ}. Find the angle of elevation of the top of the tower from a point B, 20 \mathrm{~m} nearer to A from the foot of the tower.
  6. Two buildings A and B are 100 \mathrm{~m} apart. The angle of elevation from the top of the building A to the top of the building B is 20^{\circ}. The angle of elevation from the base of the building B to the top of the building A is 50^{\circ}. Find the height of the building B.
  7. A window washer is working in a hotel building. An observer at a distance of 20 \mathrm{~m} from the building finds the angle of elevation of the worker to be of 30^{\circ}. The worker climbs up 12 \mathrm{~m} and the observer moves 4 \mathrm{~m} farther away from the building. Find the new angle of elevation of the worker.
  8. A man standing on the bank of a canal observes that the measure of the angle of elevation of a tree on the other side of the canal, is 60^{\circ}. On retreating 40 meters from the bank, he finds the measure of the angle of elevation of the tree as 30^{\circ}. Find the height of the tree and the width of the canal.

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