Trignometry
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Trigonometry is a mathematical branch focused on the study of triangles and the relationships between their sides and angles. It applies trigonometric ratios to practical problems such as calculating heights and distances, exemplified by scenarios involving towers, poles, and trees. The document also discusses concepts like angle of elevation and angle of depression in problem-solving contexts.
Trignometry
- 2. What is Trignometry? Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides.
- 3. In this topic we shall make use of Trignometric Ratios to find the height of a tree,a tower,a water tank,width of a river,distance of ship from lighthouse etc.
- 5. Line of Sight Horizontal
- 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 aeroplane from them.
- 7. Angel of Elevation Angel of Elevation
- 8. Angel of Depression If the pilot of the aeroplane looks downwards at any object on the ground then the Angle between his line of sight and horizontal line drawn away from his eyes is called Angel of Depression
- 9. Angle of Depression Horizontal Angel of Depression
- 11. Now let us Solve some problem related to Height and Distance
- 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. 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. . 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. ,
- 16. . Height of tree = + BC Hence, the height of the tree is