Question
Download Solution PDFTwo walls of equal height are on either side of a road, which is 100 m wide. At a point on the road two stairs are along the two walls in such a way that they indicate the two angles of elevation from that point at 60° and 30°. The length of the longer stair is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Distance between two walls = 100 m
Concept:
The longer stair will be AC as the corresponding side making the smaller angle is larger than that of making bigger angle.
Calculation:
Let the height of each of the walls = h
BC + CE = BE = 100
⇒ CE = 100 - BC .......(1)
In triangle ABC, AB/BC = tan 30°
⇒ h/BC = 1/√3
⇒ BC = √3h.......(2)
In triangle CDE, DE/CE = tan 60°
⇒ h/(100 - BC) = √3
h/(100 - √3h) = √3
h = 100√3 - 3h
4h = 100√3
h = 25√3 m ...... (3)
By (2) and (3)
BC = √3h = √3 × 25√3
⇒ BC = 75 m
Again in triangle ABC, BC/AC = cos 30°
⇒ 75/AC = √3/2
⇒ 150 = √3 × AC
⇒ AC = 150/√3
⇒ AC = 150/√3 ×√3/√3
∴ AC = 50√3 m
Alternate MethodBy Ratio Method
3 + 1 = 4 = 100 m
\(\Rightarrow 2√{3}= \frac{100}{4}\times 2√{3}\)
AC = 50√3
Last updated on Jun 9, 2025
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