Note on Heights and Distances

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One of the main uses of trigonometry is to find the height of an object or the distance between two points. The instruments called theodolite and sextant are used to measure certain angles and then the method of solution of triangles is used to find the required height or distance.

Angle of elevation

In the adjoining figure, O is the position of the observer, P is the position of the object and OP is the line of vision. OA is the horizontally through the observation point O. the angle AOP formed when the observer observes the object at P above horizontal line is called an angle of elevation.

Angle of depression

In the adjoining figure, O is the position of the observer, is the position of the object and P is the line of vision.

OP is the horizontal line through the observation point. The angle AOP formed when the observer observes the object at P below the horizontal line is called angle of depression.

• Angle of elevation
• Angle of depression
.

0%

81.90m

81m

71.67m

81. 97m

40 m

40.98 m

0m

59.88m

• The angle of elevation of the top of a point on the ground was observed to be 60(^o) .  On walking 60 m away from that point it was found to be 30(^o) . If the house and these points are in the same line of the same plain , find the height of the house .

100(sqrt{10})

30(sqrt{3})

90(sqrt{9})

20(sqrt{2})

11.667 m

12.68 m

12.68 Km

12.69 m

10.11 m

11.11 m

12.68 m

9.56 m

14.196 m

15.116 m

14.116 m

16.197 m

47.32 m

43. 44 m

46.77 m

48. 76 m

78.66 m

75 m

70 m

77 m

16.93 ft

13.56ft

15.99ft

12.56ft

45.45m

98.76m

98.34 m

95.62 m

45m

20m

70m

90m

76.65m

33.65m

33.81m

58.57m

78.45m

46.67m

23.45m

42.26m

278 m

462 m

264 m

267 m

182 m

298m

187 m

128 m

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kapil

AB is a straight road leading to C, the foot of a tower. A being at a distance 120 metres from C and B being 75 metres nearer. If the angle of elevation of the tower at B be the double of the angle of elevation of the tower at A, find the height of the tower.

Rijan

A wooden plank 15m long rest on the wall in such a way that it is at distance of 15÷under root2 from the foot of the ground. Find the angle made on the plank with the ground.