Question

a ladder kept inclined at angle 40 at distance 8 feet from building touches building at some height. if same ladder is kept at distance 6 feet with inclination 50 then find height at which ladder touches the building​

Answer 1

If the same ladder is kept at distance 6 feet with inclination 50 then the height at which ladder touches the building​ is 7.15 feet.

Step-by-step explanation:

Case 1:

Let the height at which the inclined ladder at an angle of 40° with the ground, touches the building be “h” feet. (As shown in the figure below).

Distance between the foot of the ladder and the building = 8 feet

According to the right-angled trigonometric ratio, we have  

tan θ = (height of the building) / base  

⇒ tan 40° = h / 8    

⇒ h = 8 * 0.839

⇒ h = 6.712 feet ….. (i)

Case 2:

Let the height at which the inclined ladder at an angle of 50° with the ground, touches the building be “(h + x)” feet. (As shown in the figure below).

Now, the distance between the foot of the ladder and the building = 6 feet

According to the right-angled trigonometric ratio, we have  

tan θ = (height of the building) / base

⇒ tan 50° = (h+x) / 6  

⇒ h+x = 6 * 1.191  

⇒ h + x = 7.15  

⇒ x = 7.15 - 6.712 ...... [from (i)]  

⇒ x = 0.438 feet

∴ h + x = 6.712 + 0.438 = 7.15 feet

Thus, the height at which the ladder touches the building is 7.15 feet.

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