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
Answers
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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