A tree of 14m height is broken by the wind so that its top touches the ground and make an angle of 60 degree with the ground. find the length of the broken part of the tree .
Answers
Answer:
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Answer:
The correct answer is : 7.5026 meters
Step-by-step explanation:
Let MN be the height of the tree, and let OP be the part of the tree that is broken by the wind. The length of OP is what we are trying to determine..
We know that the top of the tree touches the ground, which means that point M coincides with point P. We also know that the angle between the ground and the broken part of the tree is 60 degrees, which means that angle OPN is 60 degrees.
We can use trigonometry to find the length of OP. Let x be the length of OP.
Using the sine function, we have:
sin(60) = ON/OP
sqrt(3)/2 = (14-x)/x
28-2x = sqrt(3)x
28 = sqrt(3)x + 2x
28 = x(sqrt(3) + 2)
x = 28/(sqrt(3) + 2)
x = {28/(sqrt(3) + 2)} * {(sqrt(3) - 2) / (sqrt(3) - 2) }
x = 28*(sqrt(3) - 2)/(3-4)
x = 28*(2 - sqrt(3))
x = 7.5026
Therefore, the length of the broken part of the tree is approximately 7.5026 meters.
To learn more about trigonometry, visit:
https://brainly.in/question/11371684
To learn more about sinx, visit:
https://brainly.in/question/15696356
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