RD Sharma Solutions Class 10 Mathematics Solutions for Some Applications Of Trigonometry Exercise 12.1 in Chapter 12 - Some Applications Of Trigonometry
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A 1.6 m tall girl stands at a distance of 3.2 m from a lamp post and casts a shadow of 4.8 m on the ground.
Find the height of the lamp post by using properties of similar triangles.
Solution:
Triangles with the same shape but different sizes are said to be similar triangles.
In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
Let AC be the lamp post of height ‘h’
DE is the tall girl and her shadow is BE.
So, we have ED = 1.6 m, BE = 4.8 m and EC = 3.2
By using similar triangles
Since triangle BDE and triangle ABC are similar (by AA criteria), we have
\begin{aligned} &\frac{\mathrm{AC}}{\mathrm{BC}}=\frac{\mathrm{ED}}{\mathrm{BE}} \\ &\frac{\mathrm{h}}{4.8+3.2}=\frac{1.6}{4.8} \\ &\mathrm{~h}=\frac{8}{3} \mathrm{~m} \end{aligned}
Therefore, the height of the lamp post is h = 8/3 m
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