A ladder on the platform of a fire brigade van can be elevated at an angle of 70° to the maximum. the length of the ladder can be externded upto 20m. if the platform is 2m above the ground,find the maximum height from the ground upto which the ladder can reach. (sin70° =0.94)
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Step-by-step explanation:
Let AB represent the length of the ladder and AE represent the height of the platform.
Draw seg AC ⊥ seg BD.
Angle of elevation = ∠BAC = 70°
AB = 20m AE = 2m
In right-angled ∆ABC, sin 70° = BC/AB …..[By definition]
∴ 0.94 = BC/20
∴ BC = 0.94 × 20 = 18.80 m In \(\Box\)ACDE, ∠E = ∠D = 90° ∠C = 90° … [seg AC ⊥ seg BD]
∴ ∠A = 90° … [Remaining angle of \(\Box\)ACDE]
∴ \(\Box\)ACDE is a rectangle. … [Each angle is 90°]
∴ CD = AE = 2 m … [Opposite sides of a rectangle] Now, BD = BC + CD … [B – C – D] = 18.80 + 2 = 20.80 m
∴ The maximum height from the ground upto which the ladder can reach is 20.80 metrs.
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