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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?
Verified Answer
If the shadow of a boy ‘x’ metres high is 1.6m and the ang...
The given information indicates:
  • Height of the boy = x meters
  • Shadow length = 1.6 meters
  • Angle of elevation = 45 degrees
Using the trigonometric relation for a 45 degree angle 
Substitute the values:
Thus, the height of the boy is 1.6 meters.
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Community Answer
If the shadow of a boy ‘x’ metres high is 1.6m and the ang...
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.
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