a flog staff of height (a- b) stands on the top of
a tower subtends the same angle at the point on
on the horizontal plane through the food of the
tower which are as distant a & b from the tower.
the height of tower is?
Answers
Answer:
Let the angle of elevation of top of the tower subtends an angle α and the angle of elevation of top of the flag staff be β.
Let the height of tower be
′
d
′
.
⇒tan(α+θ)=
b
(d+(a−b))
,tan(β+θ)=
a
(d+(a−b))
,tanα=
b
d
,tanβ=
a
d
.
Let (d+(a−b))=p
⇒tan(α+θ)=
b
p
,tan(β+θ)=
a
p
,tanα=
b
d
,tanβ=
a
d
.
⇒(α+θ)=tan
−1
b
p
,(β+θ)=tan
−1
a
p
⇒(α−β)=tan
−1
b
p
−tan
−1
a
p
⇒(α−β)=tan
−1
(ab+p
2
)
(pa−pb)
⇒tan(α−β)=
(ab+p
2
)
(pa−pb)
⇒
1+tanαtanβ)
(tanα−tanβ)
=
(ab+p
2
)
(pa−pb)
⇒
1+
b
d
×
b
d
b
d
−
a
d
=
(ab+p
2
)
(pa−pb)
⇒
(ab+d
2
)
(ad−bd)
=
(ab+p
2
)
(pa−pb)
Since a
=b
⇒
(ab+d
2
)
d
=
(ab+p
2
)
p
⇒(abd+p
2
d)=(abp+d
2
p)
⇒(ab−pd)(d−p)=0
d=p which is impossible
⇒ab=pd
But p=d+(a−b)
⇒ab=(d+(a−b))×d
⇒d
2
+(a−b)d−ab=0
⇒d=bor−a
⇒ The height of tower is d=b
Step-by-step explanation: