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Some applications of trigonometry

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Some applications of trigonometry

  1. 1. Some Applications of Trigonometry
  2. 2. What is Trigonometry? Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
  3. 3. 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.
  4. 4. Basic Fundamentals
  5. 5. Line of Sight Horizontal
  6. 6. 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
  7. 7. • 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.
  8. 8. • 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).
  9. 9. Angle of Depression Horizontal Angel of Depression
  10. 10. Trigonometric Ratios
  11. 11. Now let us Solve some problem related to Height and Distance
  12. 12. 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
  13. 13. 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.
  14. 14. . 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
  15. 15. ,
  16. 16. . Height of tree = + BC Hence, the height of the tree is
  17. 17. 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
  18. 18. 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.
  19. 19. 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

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