1.
From the top of a minar of height 60m, the top and bottom of a clock tower are observed at the angles of
depression of 30° and 60° respectively. Then the height of the clock tower in metres is
[ ]
b) 50
c) 60
a) 40
d) 80
From
Answers
Step-by-step explanation:
10th
Maths
Some Applications of Trigonometry
Heights and Distances
From the top of a tower of ...
MATHS
From the top of a tower of height 60m, the angles of depression of the top and the bottom of a building are observed to be 30
∘
and 60
∘
respectively. Find the height of the building.
MEDIUM
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ANSWER
Let BE=h,AB=60−h,BC=ED
Distance between tower and building be ED=x
In ΔAED,tan60
∘
=
ED
AE
=
x
60
⇒
3
=
x
60
⇒x=20
3
m
In ΔABC,tan30
∘
=
BC
AB
=
20
3
60−h
⇒
3
1
=
20
3
60−h
⇒h=40m
solution
Step-by-step explanation:
Giventhat
Height of minar = 60m
Depression angles are 30° & 60°respectively.
______________________________
Let AB is minar and EC is tower .
Given, AB = 60 m and EC = ?
In triangle ABC,
Let AB = x
⇒ BD = 60 – x
And, ∠ ACB = ∠OAC (alternate angles are equal)
∠ACB = 30°
=======================
⇒We know that,
tan(theta) = p/b
tan 30° = AB/BC
1/√3=x/BC
BC=x√3............(i)
========================
⇒In ∆ADE,
∠ADE= ∠OAE(alternate angles are equal)
∠AED=60°
tan60° = AD/DE
√3=60/ DE
⇒DE = 60/√3.............(ii)
∵BC = DE
So, equation (i) = equation (ii)
x√3 = 60/√3
3x = 60
⇒x = 20m.
∵CE = BD and BD = 60 - x
CE = 60 -20
=40m
So, the height of clock tower is 40m.
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