Some Applications of Trigonometry — Questions & Answers

Sample questions from Some Applications of Trigonometry

1. Q1. Observation 7: A 25 m tree breaks so that its top touches ground 15 m from its foot. The length of remaining vertical part is:

   • A.8 m✓
   • B.15 m
   • C.10 m
   • D.25 m
   Solution

   Let remaining height h; (25−h)²=h²+15² gives 625−50h=225, so h=8 m.

2. Q2. If a building is observed from two points on the same side, the closer point has:

   • A.larger angle of elevation✓
   • B.smaller angle always
   • C.zero angle
   • D.same angle always
   Solution

   The closer observer sees a larger angle for the same height.

3. Q3. A tower is 40 m high. An object is observed at depression 60°. Its horizontal distance is:

   • A.40/√3 m✓
   • B.40√3 m
   • C.20 m
   • D.80 m
   Solution

   tan60°=40/d gives d=40/√3 m.

4. Q4. A tree breaks due to a storm and the broken part bends so that its top touches the ground, making an angle of 30° with the ground at a point 10 m from the foot of the tree. The original height of the tree is:

   • A.20 m
   • B.10√3 m✓
   • C.(20√3)/3 m
   • D.10(2 + √3) m
   Solution

   Standing part = 10 tan 30° = 10/√3 and broken part = 10/cos 30° = 20/√3; their sum is 30/√3 = 10√3 m.

5. Q5. The tops of two vertical poles, of heights 20 m and 14 m, standing on level ground are joined by a straight wire. The wire makes an angle of 30° with the horizontal. The length of the wire is:

   • A.6 m
   • B.6√3 m
   • C.12 m✓
   • D.34 m
   Solution

   C is correct. The wire rises by 20 − 14 = 6 m, and that rise is opposite the 30° angle while the wire is the hypotenuse, so the wire is 6/sin 30° = 6/(1/2) = 12 m. A gives the rise itself rather than the wire. B uses the tangent, giving the horizontal gap between the poles. D adds the two heights, which has no meaning here.

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