Page 10 - 11-Math-12 Application of Trigonometry

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Now B=C AC - AB ⇒ AC =1900 3

⇒ BC= 1900 3 - 1900= 2193.93
3

∴ Required distance = 2194 meters.

Exercise 12.3

1. A vertical pole is 8 m high and the length of its shadow is 6 m. What is the angle of
elevation of the sun at that moment?
2. A man 18 dm tall observes that the angle of elevation of the top of a tree at a distance
of 12 m from him is 32 . What is the height of the tree?
3. At the top of a cliff 80 m high, the angle of depression of a boat is 12°. How far is the
boat from the cliff?
4. A ladder leaning against a vertical wall makes an angle of 24° with the wall. Its foot is
5m from the wall. Find its length.
5. A kite flying at a height of 67.2 m is attached to a fully stretched string inclined at an
angle of 55° to the horizontal. Find the length of the string.
6. When the angle between the ground and the suri is 30°, flag pole casts a shadow of
40m long. Find the height of the top of the flag.
7. A plane flying directly above a post 6000 m away from an anti-aircraft gun observes the
gun at an angle of depression of 27°.Find the height of the plane.
8. A man on the top of a 100 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° and 19° respecting. Find the
distance between the ships.
9. P and Q are two points in line with a tree. If the distance between P and Q be 30 m and
the angles of elevation of the top of the tree at P and Q be 12° and l5° respectively, find
the height of the tree.
10 Two men are on the opposite sides of a 100 m high tower. If the measures of the
angles of elevation of the top of the tower are 18° and 22°respectively find the distance
between them.
11. A man standing 60 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° and 62° respectively. Find

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