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If the shadow of a boy ‘x’ metres high is 1.6m and the angle of elevation of the sun is 45°, then the value of ‘x’ is
- a)2m
- b)0.8m
- c)3.6m
- d)1.6m
Correct answer is option 'D'. Can you explain this answer?
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Is 5 feet long and the height of the tree he is standing next to is 20 feet, then we can use the following proportion to find the height of the boy:
Height of boy / Length of shadow of boy = Height of tree / Length of shadow of tree
Let x be the height of the boy. Then:
x / 5 = 20 / Length of shadow of tree
We need to find the length of the shadow of the tree. Since we know the length of the shadow of the boy is 5 feet, we can use similar triangles to find the length of the shadow of the tree.
The triangles formed by the boy, the tree, and their shadows are similar. That means the ratio of the height of the boy to the length of his shadow is the same as the ratio of the height of the tree to the length of its shadow:
Height of boy / Length of shadow of boy = Height of tree / Length of shadow of tree
x / 5 = 20 / Length of shadow of tree
Cross-multiplying, we get:
x * Length of shadow of tree = 100
Length of shadow of tree = 100 / x
Substituting this into the original proportion, we get:
x / 5 = 20 / (100 / x)
Simplifying, we get:
x^2 = 1000
Taking the square root of both sides, we get:
x = 31.62
So the height of the boy is approximately 31.62 feet.
Height of boy / Length of shadow of boy = Height of tree / Length of shadow of tree
Let x be the height of the boy. Then:
x / 5 = 20 / Length of shadow of tree
We need to find the length of the shadow of the tree. Since we know the length of the shadow of the boy is 5 feet, we can use similar triangles to find the length of the shadow of the tree.
The triangles formed by the boy, the tree, and their shadows are similar. That means the ratio of the height of the boy to the length of his shadow is the same as the ratio of the height of the tree to the length of its shadow:
Height of boy / Length of shadow of boy = Height of tree / Length of shadow of tree
x / 5 = 20 / Length of shadow of tree
Cross-multiplying, we get:
x * Length of shadow of tree = 100
Length of shadow of tree = 100 / x
Substituting this into the original proportion, we get:
x / 5 = 20 / (100 / x)
Simplifying, we get:
x^2 = 1000
Taking the square root of both sides, we get:
x = 31.62
So the height of the boy is approximately 31.62 feet.
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If the shadow of a boy ‘x’ metres high is 1.6m and the angle of elevation of the sun is45°, then the value of ‘x’ isa)2mb)0.8mc)3.6md)1.6mCorrect answer is option 'D'. Can you explain this answer?
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