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A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 45o. The height of the tree is:​
  • a)
    5.2 m
  • b)
    4 m
  • c)
    3 m
  • d)
    4.5 m
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A tree casts a shadow 4 m long on the ground, when the angle of elevat...
In a triangle with one angle being 90 degrees (which the tree makes with the ground) and the other being 45 degrees (the angle of elevation), the 3rd angle is bound to be 45 degrees (180 - 90 - 45 = 45). 

We also know that sides opposite to equal angles are equal.

Hence, the height of the tree will also be 4m.
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A tree casts a shadow 4 m long on the ground, when the angle of elevat...
Given:
- Length of the shadow = 4 m
- Angle of elevation of the sun = 45°

To find: Height of the tree

We can use the tangent function to solve this problem.

Let's assume the height of the tree is h meters.

Using the concept of trigonometry, we know that:

tan(angle) = opposite/adjacent

In this case, the opposite side is the height of the tree (h) and the adjacent side is the length of the shadow (4 m).

So, tan(45°) = h/4

Now, let's find the value of tan(45°):

tan(45°) = 1

Substituting this value into the equation:

1 = h/4

To solve for h, we can cross-multiply:

h = 4

Therefore, the height of the tree is 4 meters.

So, the correct answer is option 'B' (4 m).
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A tree casts a shadow 4 m long on the ground, when the angle of elevation of the sun is 45o. The height of the tree is:​a)5.2 mb)4 mc)3 md)4.5 mCorrect answer is option 'B'. Can you explain this answer?
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