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Some Applications of Trigonometry

Short Answer Type

71. In figure, what are the angles of depressions of the top and bottom of a pole from the top of a tower h m high.

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72. A balloon is connected to a meterological ground station by a cable length 215 m inclined at 60° to the horizontal determine the height of the baloon leave the ground. Assume that there is no slack in the cable.

Let AC the cable which is inclined at 60° to the horizontal
Here, we have
AC = 215 m and ∠ACB = 60°
Now, In right triangle ACB.

$Sin space 60 space equals space AB over AC rightwards double arrow space space space fraction numerator square root of 3 over denominator 2 end fraction equals AB over 215 rightwards double arrow space space space space space AB thin space equals space fraction numerator 215 cross times square root of 3 over denominator 2 end fraction rightwards double arrow space space space space space AB space space equals space fraction numerator 215 cross times 1.732 over denominator 2 end fraction rightwards double arrow space space space space space space straight h space space space equals space 186.19 space straight m$

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73. In figure, what are the angles of depression from the observing point O of the objects at P and?

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74. In figure, what are the angles of depression from the observing point O of the objects at A and B?

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75. In figure, what are angles of depression from the observing positions O₁ and O₂ of the objects at A?

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76. In figure, what are the angles of depression from the observing point O of the objects at A and B?

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77. From a point

20 square root of 3

m away from the foot of a tower, the angle of elevation of the top of the tower is 30°. Find the height of tow'er.

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78. In figure, what are the angles of depression from the observing point O of the objects at A and B?

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79. In figure, what are the angles of depression from the observing positions O₁ and O₂of the following at A?

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80. A circus artist is climbing a 20 m long rope, which is tightly stretched and teid from the top of a vertical pole to the ground? Find the height of the pole, if the angle made by the rope with the ground level is 30°.

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