The angle of elevation in this scenario can be determined by considering the relationship between the length of the shadow and the height of the man. Let's break down the explanation into the following sections:

1. Understanding the Situation:
- A man standing upright casts a shadow on the ground.
- The length of the shadow is equal to the height of the man.

2. Defining Angle of Elevation:
- The angle of elevation is the angle between the horizontal ground and the line of sight from an observer to an object above the ground.
- In this case, the object is the top of the man's head, and the line of sight is the line connecting the observer's eye to the top of the man's head.

3. Analyzing the Relationship:
- When the length of the shadow is equal to the height of the man, it forms a right-angled triangle with the man's height as the vertical side (opposite side) and the length of the shadow as the horizontal side (adjacent side).
- The hypotenuse of this right-angled triangle represents the line of sight from the observer's eye to the top of the man's head.

4. Applying Trigonometry:
- In a right-angled triangle, the tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.
- In this case, the tangent of the angle of elevation can be expressed as the ratio of the man's height to the length of the shadow.

- Mathematically, we have:
tan(angle of elevation) = opposite/adjacent
tan(angle of elevation) = height of man/length of shadow

5. Determining the Angle of Elevation:
- To find the angle of elevation, we can take the inverse tangent (arctan) of the ratio obtained in the previous step.
- This will give us the angle whose tangent is equal to the ratio of the height of the man to the length of the shadow.

- Mathematically, we have:
angle of elevation = arctan(height of man/length of shadow)

Thus, the angle of elevation can be determined by taking the inverse tangent of the ratio of the man's height to the length of his shadow.

Okay, you know the answer is 45°.

But how? Let's see.

Imagine a man standing vertically on the ground. The length of his shadow is equal to his height.

Look carefully, you can see an isosceles right-angled triangle being formed when you imagine a line connecting his real head and head of the shadow.

Two sides, i.e., his height and the length of the shadow are equal and third is the imaginary line.

Hence, the triangle has one angle measuring 90° since he is standing perpendicular on the ground and other two angles are equal since it's an isosceles triangle formed here.

Let each of those equal angles measure x°.

Now, 90°+x°+x° = 180°, since the sum of all interior angles of any triangle is 180°.
90°+2x°=180°
2x°= 180°- 90°
2x°= 90°
x°=45°

Both of the angles measure 45°. One of them is the angle of elevation. It will measure 45° anyway.

Still, an easier way to get the answer is by using the trigonometry table.

If the length of the man's shadow is equal to his height, then the ratio of his height to the length of his shadow will be doubtlessly 1. And it's a known fact that tan45° equals to 1.

Hence the required angle of elevation will be 45°.


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Hope it helps.