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Some Applications of Trigonometry

Long Answer Type

61. A statue 1.46 m. tall stands on the top of a pedestal. From a point on the ground the angle of elevation of the top of statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45° find the height of the pedestal.

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62. The angle of elevation of a jet fighter from a point A on the ground is 60°. After a flight of 15 seconds, the angle of elevation changes to 30°. If the jet is flying at a speed of 720 km/hour, find the constant height at which the jet is flying.

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63. A man on the deck of a ship 14 m above water level, observes that the angle of elevation of the top of a cliff is 60° and the angle of depression of the base of the cliff is 30°. Calculate the distance of the cliff from the ship and the height of the cliff.

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Short Answer Type

64. The height of a tower is 10 m. Calculate the height of its shadow when Sun's altitude is 45°.

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65. In the following figure, what are the angles of depression from the observing positions O₁ and O₂ of the object at A?

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66. Find the angle of elevation of the Sun's altitude when the height of shadow of a vertical pole is equal to its height.

Let the height of the pole AB = x m.
∴ Length of shadow OB ol the pole AB = x m.
Let the angle of elevation be ө, i.e.
∠AOB = ө

In Right triangle OBA, we have
$tan space straight theta space equals space AB over OB equals straight x over straight x rightwards double arrow tan space straight theta space space equals space 0 space rightwards double arrow space straight theta space equals space 45 degree$

Hence, the angle of elevation of the Sun's altitude is 45°.

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67. In figure, what are the angles of depression of depression of the top and bottom of h m tall building from the top of multistoryed building.

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68.

From a point 20 m away from the foot of a tower, the angle of elevation of the top of the tower is 30°, Find the height of the tower.

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69. In figure, what are the angles of depression from the positions O₁ and O₂ of the object at A?

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70.

The string of akite is 100 m long and its makes an angle of 60° with the horizontal. Find the height of the kite. Assume that there is no slackness in the string.

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