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Some applications of trigonometry
Some
Applications of
Trigonometry
What is Trigonometry?
Trigonometry is a branch
of mathematics that studies triangles and the
relationships between their sides and the angles
between these sides.
In this topic we shall make use of
Trigonometric Ratios to find the height of
a tree, a tower, a water tank, width of a
river, distance of ship from lighthouse etc.
Basic Fundamentals
Line of Sight

Horizontal
Angle of Elevation
The angle which the line of sight
makes with a horizontal line drawn
away from their eyes is called the
angle of Elevation of aero plane from
them.

Angel of Elevation
• Angle of Elevation: In the picture below, an
observer is standing at the top of a building is
looking straight ahead (horizontal line). The
observer must raise his eyes to see the airplane
(slanting line). This is known as the angle of
elevation.
• Angle of Depression: The angle below horizontal that an
observer must look to see an object that is lower than
the observer. Note: The angle of depression is congruent
to the angle of elevation (this assumes the object is close
enough to the observer so that the horizontals for the
observer and the object are effectively parallel).
Angle of Depression

Horizontal

Angel of Depression
Trigonometric Ratios
Now let us Solve some
problem related to
Height and Distance
The angle of elevation of the top of a tower from a
point on the ground, which is 30 m away from the
foot of the tower is 30°. Find the height of the tower.
.

Let AB be the tower and the angle of elevation from point C
(on ground) is
30°.
In ΔABC,

Therefore, the height of the tower is
A circus artist is climbing a 20 m long rope, which is tightly
stretched and tied from the top of a vertical pole to the
ground. Find the height of the pole, if the angle made by the
rope with the ground level is 30 °.
Sol:- It can be observed from the figure that AB is the pole.
In ΔABC,

Therefore, the height of the pole is 10 m.
.

Let K be the kite and the string is tied to point P on
the ground.
In ΔKLP,

Hence, the length of the string is
,
.

Height of tree =

+ BC

Hence, the height of the tree is
Some applications of trigonometry
Some applications of trigonometry
1

Tan 30

h

3
Tan 60

h

3
d

From (1) d

(1)

d

The angle of elevation of the top of a tower from a
point At the foot of the tower is 300 . And after
advancing 150mtrs Towards the foot of the tower, the
angle of elevation becomes 600 .Find the height of
the tower
(2)

150

h 3

From ( 2 )
3 (d

h

150 )

h

30

60

Substituti ng ..the ..value ..of .. d ..
3 (h 3
3h

150

3h

h

2h

150

h

150 )
3

h

150

h

3

d

3

75 * 1 . 732

150

129 . 9 m
Questions based on trigonometry :• The angle of elevation of the top of a pole measures 48° from a point on
the ground 18 ft. away from its base. Find the height of the flagpole.
• Solution
Step 1: Let’s first visualize the situation
Step 2: Let ‘x’ be the height of the flagpole.
STEP 3: From triangle ABC,tan48=x/18
Step 4: x = 18 × tan 48° = 18 × 1.11061… = 19.99102…» 20
Step 5: So, the flagpole is about 20 ft. high.
C
A

50

D

45

A hoarding is fitted above a building. The height of the
building is 12 m. When I look at the lights fitted on top
of the hoarding, the angle of elevation is 500 and when I
look at the top of the building from the same place, the
angle is 450. If the height of the flat on each floor is
equal to the height of the hoarding, the max floors on
the building are? (Tan 500=1.1917)

B

ANSWER : Let AB denote the height of the building,
Let AC denote the height of the hoarding on top of the building
Thus, Tan500 = (12 + AC) ÷ 12
1.1917 = 1 + (AC ÷ 12)
1.1917 – 1 = AC ÷ 12
12 ÷ AC = 1 ÷ 0.1917 ~ 5
Some applications of trigonometry
Some applications of trigonometry

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Some applications of trigonometry

  • 3. What is Trigonometry? Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
  • 4. In this topic we shall make use of Trigonometric Ratios to find the height of a tree, a tower, a water tank, width of a river, distance of ship from lighthouse etc.
  • 7. Angle of Elevation The angle which the line of sight makes with a horizontal line drawn away from their eyes is called the angle of Elevation of aero plane from them. Angel of Elevation
  • 8. • Angle of Elevation: In the picture below, an observer is standing at the top of a building is looking straight ahead (horizontal line). The observer must raise his eyes to see the airplane (slanting line). This is known as the angle of elevation.
  • 9. • Angle of Depression: The angle below horizontal that an observer must look to see an object that is lower than the observer. Note: The angle of depression is congruent to the angle of elevation (this assumes the object is close enough to the observer so that the horizontals for the observer and the object are effectively parallel).
  • 12. Now let us Solve some problem related to Height and Distance
  • 13. The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is 30°. Find the height of the tower. . Let AB be the tower and the angle of elevation from point C (on ground) is 30°. In ΔABC, Therefore, the height of the tower is
  • 14. A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole, if the angle made by the rope with the ground level is 30 °. Sol:- It can be observed from the figure that AB is the pole. In ΔABC, Therefore, the height of the pole is 10 m.
  • 15. . Let K be the kite and the string is tied to point P on the ground. In ΔKLP, Hence, the length of the string is
  • 16. ,
  • 17. . Height of tree = + BC Hence, the height of the tree is
  • 20. 1 Tan 30 h 3 Tan 60 h 3 d From (1) d (1) d The angle of elevation of the top of a tower from a point At the foot of the tower is 300 . And after advancing 150mtrs Towards the foot of the tower, the angle of elevation becomes 600 .Find the height of the tower (2) 150 h 3 From ( 2 ) 3 (d h 150 ) h 30 60 Substituti ng ..the ..value ..of .. d .. 3 (h 3 3h 150 3h h 2h 150 h 150 ) 3 h 150 h 3 d 3 75 * 1 . 732 150 129 . 9 m
  • 21. Questions based on trigonometry :• The angle of elevation of the top of a pole measures 48° from a point on the ground 18 ft. away from its base. Find the height of the flagpole. • Solution Step 1: Let’s first visualize the situation Step 2: Let ‘x’ be the height of the flagpole. STEP 3: From triangle ABC,tan48=x/18 Step 4: x = 18 × tan 48° = 18 × 1.11061… = 19.99102…» 20 Step 5: So, the flagpole is about 20 ft. high.
  • 22. C A 50 D 45 A hoarding is fitted above a building. The height of the building is 12 m. When I look at the lights fitted on top of the hoarding, the angle of elevation is 500 and when I look at the top of the building from the same place, the angle is 450. If the height of the flat on each floor is equal to the height of the hoarding, the max floors on the building are? (Tan 500=1.1917) B ANSWER : Let AB denote the height of the building, Let AC denote the height of the hoarding on top of the building Thus, Tan500 = (12 + AC) ÷ 12 1.1917 = 1 + (AC ÷ 12) 1.1917 – 1 = AC ÷ 12 12 ÷ AC = 1 ÷ 0.1917 ~ 5