If a 1.5 m tall girl stands at a distance of 3m from a lamp-post and casts a shadow of length 4.5m on the ground, then the height of the lamp-post is
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We are given:
Height of the girl = 1.5 m,
Distance of the girl from the lamp-post = 3 m,
Length of the shadow cast by the girl = 4.5 m.
Use similar triangles
The height of the lamp-post (H) and the total length of the shadow (distance from the base of the lamp-post to the end of the shadow) form a larger triangle. The height of the girl and her shadow form a smaller, similar triangle.
From similar triangles:
(Height of lamp-post) / (Total shadow length) = (Height of girl) / (Length of girl’s shadow).
Substitute the values:
H / (3 + 4.5) = 1.5 / 4.5.
Simplify:
H / 7.5 = 1.5 / 4.5.
Solve for H
Simplify the ratio on the right-hand side:
1.5 / 4.5 = 1/3.
Thus:
H / 7.5 = 1/3.
Multiply through by 7.5:
H = 7.5 × (1/3) = 2.5 m.
This question related to Chapter 9 Mathematics Class 10th NCERT. From the Chapter 9 Applications of Trigonometry. Give answer according to your understanding.
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