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Mohit is standing at some distance from a 60 meters tall building. Mohit is 1.8 meters tall. When Mohit walks towards the building, then the angle of elevation from his head becomes 60° from 45°. How much distance (in metres) Mohit covered towards the building?

Mohit is standing at some distance from a 60 meters tall building. Mohit is 1.8 meters tall. When Mohit walks towards the building, then the angle of elevation from his head becomes 60° from 45°. How much distance (in metres) Mohit covered towards the building? Correct Answer 19.4 (3 - √3)

Given :

Mohit is 1.8 m tall and standing at some distance from 60 m high building

Calculations :

We can use the following table for the values of trigonometric functions at specific values of angle θ:

[ alt="Trigo - Angles and Radian" src="//storage.googleapis.com/tb-img/production/21/02/Trigo%20-%20Angles%20and%20Radian.PNG" style="width: 392px; height: 218px;">

[ alt="F1 Ashish Singh Anil 24.02.21 D30" src="//storage.googleapis.com/tb-img/production/21/02/F1_Ashish%20Singh_Anil_24.02.21_D30.png" style="width: 314px; height: 218px;">

According to the question 

Height of Mohit(CF) = 1.8 m 

Now ∆ABC 

tan45° = AB/BC 

⇒ BC = AB 

⇒ BC = 58.2 m

In ∆ABL 

tan60° = AB/BL 

⇒ BL = AB/√3 

⇒ BL = 19.4√3 

Distance(LC) covered by Mohit = BC - BL 

⇒ 58.2 - 19.4√3 

⇒ 19.4(3 - √3) m 

∴ Total distance covered by Mohit is 19.4(3 - √3) m 

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