Trigonometrical Ratios And Identities Ques 6
- Two vertical poles of heights, $20 \mathrm{m}$ and $80 \mathrm{m}$ stand apart on a horizontal plane. The height (in $\mathrm{m}$ ) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is
(2019 Main, 8 April II)
(a) $15$
(b) $16$
(c) $12$
(d) $18$
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Answer:
Correct Answer: 6.(b)
Solution: (b) Let a first pole $A B$ having height $20 \mathrm{m}$ and second pole $P Q$ having height $80 \mathrm{m}$ and
$\angle P B Q=\alpha, \angle A Q B=\beta$
and $M N=h m$ is the height of intersection point from the horizontal plane
$\because \quad \tan \alpha=\frac{h}{x}=\frac{80}{x+y}\quad \quad [$ in $\triangle M N B$ and $\triangle P Q B]$ $\quad$ ……..(i)
and $\quad \tan \beta=\frac{h}{y}=\frac{20}{x+y}\quad \quad $ [in $\triangle M N Q$ and $\triangle A B Q]$ $\quad$ ……..(ii)
From Eqs. (i) and (ii), we get
$ \frac{y}{x}=4 \Rightarrow y=4 x $ $\quad$ ……..(iii)
From Eqs. (i) and (iii), we get
$ \frac{h}{x}=\frac{80}{x+4 x} \Rightarrow h=\frac{80}{5}=16 \mathrm{m} $
BETA
