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A tree is broken by the wind. Its top struck the ground at an angle 30° at a distance of 30 m from its foot. The whole height of the tree is :
- a)10 √3 m
- b)20 √3 m
- c)40 √3 m
- d)30 √3 m .
Correct answer is option 'D'. Can you explain this answer?
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A tree is broken by the wind. Its top struck the ground at an angle 30...
Degrees from the vertical. The broken section of the tree makes an angle of 60 degrees with the ground. What is the height of the tree before it was broken?
Let's call the height of the tree "h" and the distance from the base of the tree to where it broke "x". We can use trigonometry to solve for these values.
First, we can use the angle of 30 degrees to find the length of the broken section of the tree, which we'll call "y". Using the sine function:
sin(30) = y/h
y = h*sin(30)
y = 0.5h
Next, we can use the angle of 60 degrees and the Pythagorean theorem to find the length of the entire broken section of the tree (including the part still standing). Let's call this length "z".
cos(60) = x/z
z = x/cos(60)
z = 2x
Using the Pythagorean theorem:
z^2 = y^2 + h^2
(2x)^2 = (0.5h)^2 + h^2
4x^2 = 0.25h^2 + h^2
4x^2 = 1.25h^2
h^2 = 4x^2/1.25
h^2 = 3.2x^2
h = sqrt(3.2)x
So the height of the tree before it was broken is equal to the square root of 3.2 times the distance from the base to where it broke. We don't have a specific value for x, so we can't give an exact height, but we can say that it's proportional to the square root of 3.2x.
Let's call the height of the tree "h" and the distance from the base of the tree to where it broke "x". We can use trigonometry to solve for these values.
First, we can use the angle of 30 degrees to find the length of the broken section of the tree, which we'll call "y". Using the sine function:
sin(30) = y/h
y = h*sin(30)
y = 0.5h
Next, we can use the angle of 60 degrees and the Pythagorean theorem to find the length of the entire broken section of the tree (including the part still standing). Let's call this length "z".
cos(60) = x/z
z = x/cos(60)
z = 2x
Using the Pythagorean theorem:
z^2 = y^2 + h^2
(2x)^2 = (0.5h)^2 + h^2
4x^2 = 0.25h^2 + h^2
4x^2 = 1.25h^2
h^2 = 4x^2/1.25
h^2 = 3.2x^2
h = sqrt(3.2)x
So the height of the tree before it was broken is equal to the square root of 3.2 times the distance from the base to where it broke. We don't have a specific value for x, so we can't give an exact height, but we can say that it's proportional to the square root of 3.2x.
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A tree is broken by the wind. Its top struck the ground at an angle 30° at a distance of 30 mfrom its foot. The whole height of the tree is :a)10 √3mb)20 √3mc)40 √3md)30 √3m .Correct answer is option 'D'. Can you explain this answer?
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