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प्रश्न
Read the following passage and answer the questions given below.
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Qutub Minar, located in South Delhi, India was built in the year 1193. It is 72 m high tower. Working on a school project, Charu and Daljeet visited the monument. They used trigonometry to find their distance from the tower. Observe the picture given below. Points C and D represent their positions on the ground in line with the base of tower, the angles of elevation of top of the tower (Point A) are 60° and 45° from points C and D respectively.
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- Based on the above information, draw a well-labelled diagram.
- Find the distances CD, BC and BD. [use `sqrt(3)` = 1.73]
उत्तर
1.
2.
In ΔABC, tan 60° = `("AB")/("BC")`
⇒ `sqrt(3) = 72/("BC")`
⇒ BC = `72/sqrt(3) = 24sqrt(3)`
= 24 × 1.73
⇒ BC = 41.52 m
In ΔABD, ∠B = 90°
tan 45° = `("AB")/("BD")`
BD = AB
BD = 72 m
Now, CD = BD – BC
= 72 – 41.52
CD = 30.48 m
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संबंधित प्रश्न
From the top of a building 30 m high, the top and bottom of a tower are observed to have angles of depression 30º and 45º respectively. Find the height of the tower
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One evening, Kaushik was in a park. Children were playing cricket. Birds were singing on a nearby tree of height 80m. He observed a bird on the tree at an angle of elevation of 45°. When a sixer was hit, a ball flew through the tree frightening the bird to fly away. In 2 seconds, he observed the bird flying at the same height at an angle of elevation of 30° and the ball flying towards him at the same height at an angle of elevation of 60°.
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- At what distance from the foot of the tree was he observing the bird sitting on the tree?
- How far did the bird fly in the mentioned time?
(or)
After hitting the tree, how far did the ball travel in the sky when Kaushik saw the ball? - What is the speed of the bird in m/min if it had flown `20(sqrt3 + 1) m`?
