A ladder on the platform of a fire brigade van can be elevated at an angle of 60° to the
maximum. The length of the ladder can be extended upto 40 m. If the platform is 2.5 m
above the ground, find the maximum height from the ground upto which the ladder can
reach. ( √3 = 1.73)
Answers
here your answer⤵️
➡️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 ◼️ACDE,
∠E = ∠D = 90°
∠C = 90° … [seg AC ⊥ seg BD]
∴ ∠A = 90° … [Remaining angle of □◻ACDE]
∴ ◼️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.⬅️
step by step explanation ✅
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