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प्रश्न
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Case Study Trigonometry in the form of triangulation forms the basis of navigation, whether it is by land, sea or air. GPS a radio navigation system helps to locate our position on earth with the help of satellites. |
- Make a labelled figure on the basis of the given information and calculate the distance of the boat from the foot of the observation tower.
- After 10 minutes, the guard observed that the boat was approaching the tower and its distance from tower is reduced by 240(`sqrt(3)` - 1) m. He immediately raised the alarm. What was the new angle of depression of the boat from the top of the observation tower?
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उत्तर
i.
In ∆PTR, tan 30° = `240/x` ⇒ x = `240sqrt(3)` m
ii. Distance of boat from tower = `240sqrt(3) - 240(sqrt(3) - 1)` = 240 m
Let the angle of depression = θ
tan θ = `240/240` = 1 ⇒ θ = 45°
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Case Study -2
A hockey field is the playing surface for the game of hockey. Historically, the game was played on natural turf (grass) but nowadays it is predominantly played on an artificial turf.
It is rectangular in shape - 100 yards by 60 yards. Goals consist of two upright posts placed equidistant from the centre of the backline, joined at the top by a horizontal crossbar. The inner edges of the posts must be 3.66 metres (4 yards) apart, and the lower edge of the crossbar must be 2.14 metres (7 feet) above the ground.
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- Midfielders: As shown by players E, F and G.
- Fullbacks: As shown by players H, I and J.
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Using the picture of a hockey field below, answer the questions that follow:
The point on y axis equidistant from B and C is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
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Read the following passage:
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Alia and Shagun are friends living on the same street in Patel Nagar. Shagun's house is at the intersection of one street with another street on which there is a library. They both study in the same school and that is not far from Shagun's house. Suppose the school is situated at the point O, i.e., the origin, Alia's house is at A. Shagun's house is at B and library is at C. |
Based on the above information, answer the following questions.
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- Show that for Shagun, school is farther compared to Alia's house and library.
OR
Show that Alia’s house, shagun’s house and library for an isosceles right triangle.
