QUESTION :
The elevation of the top of a temple from a point A situated in south is 45° and B is a point to the west of the point A. Also if the elevation of the top of the temple from B is 15° and AB = 2a, then find the height of the temple.
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Answers
Question :-
The elevation of the top of a temple from a point A situated in south is 45° and B is a point to the west of the point A. Also if the elevation of the top of the temple from B is 15° and AB = 2a, then find the height of the temple.
Answer :-
Let's assume the height of the temple = h
in △ APO –
=> tan(45⁰) = h/(AP)
=> AP = h
in △ BPO –
=> tan(15⁰) = h/(BP)
=> 2 - √3 = h/(BP)
=> BP = h/(2 - √3)
=> BP = [h/(2 - √3)][(2 + √3)/(2 + √3)
=> BP = h(2 + √3)
Now , Applying pythagoras theorm in △ PAB
=> (BP)² = (AP)² + (AB)²
=> [h(2 + √3)]² = h² + (2a)²
=> h²(2 + √3)² = h² + 4a²
=> h²(4 + 3 + 4√3) = h² + 4a²
=> h²(7 + 4√3) = h² + 4a²
=> h²(7 + 4√3 - 1) = 4a²
=> h²(6 + 4√3) = 4a²
=> h² = (4a²)/(6 + 4√3)
=> h = a[2/√(6 + 4√3)]
Therefore the height of the temple is a[2/√(6 + 4√3)].
Step-by-step explanation:
Answer
In ΔADC
tan30
o
=
AC
DC
3
1
=
d
h
........(1)
d=
3
h
→d=
3
×10
3
=30m
In ΔBCD
tan60
o
=
BC
DC
3
=
d−20
h
.......(2)
on solving equation (1) & (2)
3
=
3
h−20
h
⇒3h−20
3
=h
2h=20
3
h=10
3
m
height of tower.
solution