Maharashtra State Board course SSC (English Medium) Class 10th Board Exam
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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 Extended Upto 20 M. If the Platform is 2m Above the Ground - Geometry

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Question

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 extended upto 20 m. If the platform is 2m above the ground, find the maximum height from the ground upto which the ladder can reach. (sin 70° = 0.94)

Solution

Let AB be the platform of the fire brigade van and AD be the ladder. 
Suppose the maximum height from the ground upto which the ladder can reach be h m.

Here, AB = 2 m, AD = 20 m, ∠DAE = 70º and AE ⊥ CD.
DE = CD − CE = (h − 2) m             (CE = AB)
In right ∆AED,
\[\sin70^\circ = \frac{DE}{AD}\]
\[ \Rightarrow 0 . 94 = \frac{h - 2}{20}\]
\[ \Rightarrow h - 2 = 20 \times 0 . 94 = 18 . 8\]
\[ \Rightarrow h = 18 . 8 + 2 = 20 . 8 m\]

Thus, the maximum height from the ground upto which the ladder can reach is 20.8 m.

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APPEARS IN

 Balbharati Solution for Balbharati Class 10 Mathematics 2 Geometry (2018 to Current)
Chapter 6: Trigonometry
Problem set 6 | Q: 9 | Page no. 139
Solution 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 Extended Upto 20 M. If the Platform is 2m Above the Ground Concept: Heights and Distances.
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