Mohit is standing at some distance from a 60-meter tall building. Mohit is 1.8-metre tall. When Mohit walks towards the building, the angle of elevation from his head becomes 60° from 45°. How much distance (in meters) does Mohit cover towards the building?a)18.6(4 - √3)b)58.2 - 24.6 √3c)19.4(√3 + 1)d)19.4(3 - √3)Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Given information:
- Mohit is standing at a certain distance from a 60-meter tall building.
- Mohit's height is 1.8 meters.
- The angle of elevation from Mohit's head to the top of the building changes from 45° to 60° as Mohit walks towards the building.
- We need to find the distance Mohit covers towards the building.

Let's solve this step by step:

1. Understanding the problem:
- The angle of elevation is the angle formed between the line of sight and the horizontal line.
- As Mohit walks towards the building, the angle of elevation increases from 45° to 60°.
- We need to find the distance Mohit covers towards the building.

2. Breaking down the problem:
- We can consider two right-angled triangles in this scenario:
- Triangle 1: Mohit's initial position, with an angle of elevation of 45°.
- Triangle 2: Mohit's final position, with an angle of elevation of 60°.
- We need to find the difference in distance covered by Mohit towards the building in these two positions.

3. Calculating the distance covered:
- Let the initial distance of Mohit from the building be x meters.
- In Triangle 1, the opposite side (height of the building) is 60 meters, and the adjacent side is x meters.
- In Triangle 2, the opposite side (height of the building) is still 60 meters, and the adjacent side is (x - d) meters, where d is the distance Mohit covers towards the building.
- Using the tangent function, we can write the following equations:
- tan(45°) = 60 / x
- tan(60°) = 60 / (x - d)
- We can solve these two equations to find the value of d.

4. Solving the equations:
- tan(45°) = 1, and tan(60°) = √3.
- Substituting these values in the equations, we get:
- 1 = 60 / x
- √3 = 60 / (x - d)
- Rearranging the equations, we get:
- x = 60
- x - d = 60 / √3
- Solving these equations, we find:
- d = x - x / √3
- d = x(1 - 1 / √3)
- d = x(√3 - 1) / √3
- d = 60(√3 - 1) / √3
- d = 60(3 - √3) / 3√3
- d = 20(3 - √3) / √3
- d = 20(3√3 - √3) / 3
- d = 20(2√3) / 3
- d = 40√3 / 3
- d ≈ 23.09 meters

5. Final answer:
- Mohit covers approximately 23.09 meters towards the building.

Answer

Height of the building from the head of Mohit = 60 - 1.8 = 58.2 m

Case I: When the angle of elevation is 45°

Distance from building (AC) = 58.2 m

Case II: When the angle of elevation is 60°

Distance from the building (BC) =

Distance covered by Mohit (AB) = AC - BC =

= (19.4 × 3) - (19.4 × √3)

= 19.4 (3 - √3)m

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