Trigonometry application

TRIGONOMETRY
STD X
MAHARASHTRA STATE BOARD OF EDUCATION,
MUMBAI
APPLICATIONS - TO FIND HEIGHT AND DISTANCE

APPLICATION (TO FIND HEIGHT AND DISTANCE)
ANGLE OF ELEVATION
ANGLE OF DEPRESSION
Sin =
𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
cos=
𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
tan =

APPLICATION ( TO FIND HEIGHT AND DISTANCE)
sin =
cos =
tan =
GIVEN: BC = distance = 80m
AB = height of the tower ?
∠ 𝐴𝐶𝐵 = 45 = 𝑎𝑛𝑔𝑙𝑒 𝑜𝑓 𝑒𝑙𝑒𝑣𝑒𝑎𝑡𝑖𝑜𝑛
tan C =
𝑜𝑝𝑝
𝑎𝑑𝑗
tan 45=
𝐴𝐵
𝐵𝐶
1=
𝐴𝐵
80
AB = 80 m
Solve: A person is standing at a distance of 80 m from a building
looking at its top. The angle of elevation is 450. Find the height of the
building.
Height of the building is 80 m

Sin =
cos =
tan =
GIVEN: AB = height of the
tree, broke at D, broken
part touched at C on the
ground making an angle
of 60o. BC = 20 m
tan 60 =
𝑜𝑝𝑝
𝑎𝑑𝑗
=
𝐷𝐵
𝐵𝐶
= 3 =
𝐷𝐵
20
= 20 3 = DB
sin 60 =
𝑜𝑝𝑝
ℎ𝑦𝑝
=
3
2
=
3 𝑋 20
𝐻𝑌𝑃
HYP =
3 X 20 X 2
3
HYP = 40
HENCE TOTAL HEIGHT
= DB + DC
= (20 3 +40) m
SOLVE: A storm broke a tree and the treetop rested 20m from the base of the tree,
making an angle of 600 with the horizontal. Find the height of the tree.
Height of the tree is (20 3 +40) m

GIVEN: AB is the lighthouse, height = 90 m,
observer is at A looking at the ship at C making
an angle of 600 with horizontal. (angle of
depression)
m∠ ACB = 60 (alternate angle)
in triangle ABC,
tan 60 =
𝐴𝐵
𝐵𝐶
3 =
90
𝐵𝐶
BC =
90
3
X
3
3
BC = 30 3 m
sin =
cos =
tan =
From the top of a lighthouse, an observer looking at a ship makes angle of depression of 600. If the height
of the lighthouse is 90 m, then find how far the ship is from the lighthouse.
The ship is 30 3 m
From the lighthouse.

GIVEN: AB and CD are poles of length 18m
and 7 m, string AC =22 m. find m∠ACE
ECDB is a rectangle. EB = CD =7 m
Hence, AE = (18-7) m = 11 m
Sin C =
𝐴𝐸
𝐸𝐶
=
11
22
=
1
2
But sin 300 =
1
2
HENCE, m∠ACE = 300
Sin =
cos =
tan =
Two poles of heights 18m and 7 m are erected on a ground. The length of the wire fastened at their tops
in 22 m. Find the angle made by the wire with the horizontal.

GIVEN: ED = width of the road, CD = height of one building = 10 m,
m∠ ACB = 600 (angle of elevation), AE = height of another building ?
BCDE is a rectangle, BC = ED = 12 m, BE = CD = 10 m
In triangle ABC, tan 60 =
𝐴𝐵
𝐵𝐶
= 3 =
𝐴𝐵
12
AB = 12 3
HENCE, AE = (12 3 +10 ) m
Sin =
cos =
tan =
Two buildings are facing each other on a road of width 12 m, From the top of the first building, which is
10m high, the angle of elevation of the top of the second is found to be 600. What is the height of the
second building?
The height of the second building is( 12 3 +10 ) m

Sin =
cos =
tan =
GIVEN: AB = 60 m, string AC = ? m∠ ACB =
60 (angle of elevation)
sin 60 =
𝐴𝐵
𝐴𝐶
3
2
=
60
𝐴𝐶
AC =
60 𝑥 2
3
X
3
3
AC =
120 3
3
= 40 3 m
A kite is flying at a height of 60m above the ground. The string attached to the kite is tied at the
ground. It makes an angle of 600with the ground. Assuming that the string is straight, find the length of
the string.
The length of the string is 40 3 m

While landing at an aeroplane, a pilot made an angle of depression of 200. Average speed of the plane was 200 km /hr.
the plane reached the ground after 54 seconds, Find the height at which the plane was when it started landing.
A
GIVEN: landing path of an
aeroplane is AC, lands with
the speed of 200 km/hr
taking 54 sec.
To find: AB – height at
which aeroplane was at the
time of landing.
𝑚∠𝐴𝐶𝐵 = 𝑚∠𝐷𝐴𝐶 = 200
(ALTERNATE ANGLE)
Calculate distance covered
in 54 sec:
200 km is covered in 1 hour (60 X 60 sec)
? km is covered in 54 sec
=
54 𝑋 200
60 𝑋 60
= 3 km
Hence
Sin 200 =
𝐴𝐵
𝐴𝐶
0.342 =
𝐴𝐵
3
AB = 1.026 km
B
The plane is at a height of 1.026 km at the time of landing.

A ladder on the platform of a fire brigade van can be elevated at an angle of 700 to the maximum. The
length of the ladder can be extended up to 20 m. If the platform is 2m above the ground, find the
maximum height from the ground up to which the ladder can reach. (sin 700 =0.94)
GIVEN: AB is the ladder of height 20 m, BD is a height of
platform of 2 m above ground
To find: AE , maximum height ladder reaches.
Sin 70 =
𝐴𝐶
𝐴𝐵
0.94 =
𝐴𝐶
20
AC = 20 x 0.94
= 18.80 m
HENCE, AE = 18.80 + 2 = 20.80 m
The max height from the ground up to
which ladder can reach is 20.80 m

Trigonometry application

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Trigonometry application