Slide 1 : Suppose the students of a school are visiting Qutub Minar. Now, if a student looking at the top of the Minar,can the student find out the height of the Minar,without actually measuring it?
Slide 2 : Suppose a girl is sitting on the balcony of her house located on the bank of a river. She is looking down at a flowerpot placed on a stair of a temple situated nearby on the other bank of the river. If she Knows the height of the building ,can she find out the width of the river
Slide 3 : TRIGONOMETRY
Slide 4 : In all the situations given above, the distances or heights can be found by using some mathematical techniques, which come under a branch of mathematics called' trigonometry’. The word ‘trigonometry’ is derived from the Greek words ‘tri’(meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning measure). In fact,
trigonometry is the study of relationships between the sides and angles of a right triangle
Slide 5 : Ratios of the sides of a right triangle with respect to its acute angles, called trigonometric ratios of the angle.
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Slide 7 : Find cosP,sinP,tanP from the given figure
Find cos ,sin , tan from the fig : Find cos ,sin , tan from the fig ? ? ?
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Slide 11 : If tan B=3/4 find sinB,cosB A B C
Slide 12 : If sin A =8/10 find tanA , cos A A B C
Slide 13 : Application of trigonometry in different situations The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer. The angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e., the case when we raise our head to look at the object
Slide 14 : The girl sitting on the balcony is looking down at a flower pot placed on a stair of the temple. In this case, the line of sight is below the horizontal level. The angle so formed by the line of sight with the horizontal is called the angle of depression i.e., the case when we lower our head to look at the point being viewed
Slide 15 : Example 1 : A tower stands vertically on the ground. From a point on the ground,which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. Find the height of the tower.
Slide 16 : Example 2 : An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is 45°. What is the height of the chimney?
Slide 17 : Example 3: From a point on a bridge cross a river, the angles of depression of the banks on opposite sides of the river are 30° and 45°, respectively. If the bridge is at a height of 3 m from the banks, find the width of the river.
Slide 18 : Example 4:From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Determine the height of the tower.