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TO E-LESSON DAY’S LESSON PRESENTED BY ASHIM NATH PGT(MATHS) J N V HARINAGAR KARIMGANJ ASSAM To Develop Thinking , Analytical , Geometrical Concept Of Mathematics To Appriciate Development Of Mathematics Subject In Various Fields. To Understand Importance Of Mathematics In Day To Day Life. KNOWLEDGE To acquaint students about the concept of angle of elevation and angle of depression UNDERSTANDING To understand the method of finding height and distance APPLICATION To apply the acquired knowledge to find the height and distance of tower , building , width of river. etc. SKILL To develop skill of drawing the diagram of the problems PREVIOUS KNOWLDEGE PREVIOUS KNOWLDEGE SEE THESE FIGURES IN THE BOX FIND THE RIGHT ANGLE TRIANGLE THIS IS THE RIGHT ANGLED TRIANGLE IN THIS RIGHT TRIANGLE B =900 A AC=h, OPPOSITE TO RIGHTANGLE B H YP h PERPENDICULAR O ACB=θ TU N SE p AB= p BC=b θ B C b BASE PANDIT BADIRE PRASAD Sin θ= P h HARI HARI BOLA Cos θ= b h tan θ = p b H YP h PERPENDICULAR cosec θ = h p O TN U SE sec θ = h b p cot θ =b p θ B b BASE HOW DO YOU MAKE TABLE OF HOW DO YOU MAKE TABLE OF TRIGNOMETRIC RATIO ANGLES TRIGNOMETRIC RATIO ANGLES 1 WRITE DIGITS, 0 ,1, 2, 3, 4. 2 DIVIDE EACH DIGIT BY 4.ie 3 TAKING SQURE ROOT OF EACH SEPERATELY ANGLES /RATIOS 0 60 30 45 90 sinθ 0 1/ 2 1/ 2 3/2 1 Cosθ 3/2 1/ 2 1/2 1 0 Tanθ 0 1/ 3 1 3 N.D Cosecθ N.D 2 2 2/ 3 1 secθ 1 2/ 3 2 2 N.D cotθ 0 3 1 1/ 3 0 HORIZONTAL LINE THE LINE PASSING THROUGH THE OBSERVER IS CALLED HORIZONTAL LINE OBJECT IS ABOVE THE object HORIZONTAL LINE HORIZONTAL LINE OBJECT OBJECT ISBELOW THE OBSERVER HORIZONTAL LINE OBSERVER LI NE OF SI GH T THE LINE JOINING OBSERVER AND OBJECT OBJECT IS CALLED LINE OF SIGHT A tower stands vertically on the ground. From a point on the ground 20m away from the foot of the tower the angle of elevation of the tower is 600. what is the height of the tower? DIAGRAM SOLUTION Let AB=h, height of the tower Given BC= 20m, C = 60 A In right angled triangle ABC Tanθ=perpendicular / base Tan 60 = AB / BC 3 =h/20 H = 20 ×. 3 = 20 ×1.732 600 = 3.4640 C 20m B WHEN THE OBJECT WILL BE ABOVE HORIZONTAL LINE THEN ANGLE FORMED BETWEEN THE LINE OF SIGHT AND HORIZONTAL IS CALLED HT SIG OF I NE L HORIZONTAL LINE ANGLE OF ELEVATION ANGLE OF ELEVATION LINE OF SIGHT HORIZONTAL LINE WHEN THE OBJECT WILL BE ABOVE HORIZONTAL LINE THEN ANGLE HORIZONTAL LINE FORMED BETWEEN THE LINE OF SIGHT AN GLE AND LI OF DPR HORIZONTAL IS NE ESS CALLED OF I ON SI GHT A flag staff stands on the top of a 5m high tower . From a point on the ground , the angle of elevation at the top of the flag staff is 600 and from the same point , the angle of elevation of the top of the tower is 450 . Find the length of the flag staff. A SOLUTION H GIVEN BC=5m, heightof tower. C letAC=H be the height of the tower 5m ADB=60 0 600 450 CDB=450 B D CONTINUE Tanθ= p / b In CBD, Tan450=BC/ BD 1=5 / BD BD= 5 In ABD, Tan 600 =AB/ BD 3 = (AC+ BC)/ BD 3 = (H+5) /5 H = 5 ( 3 – 1) QUESTION D From a point on the ground 40m, from the foot of a tower , the angle of elevation to the top Of the tower is 300 the C angle of the elevation to the top of the water tank On the top of the tower is 450.find the height of the tower and A B the depth of the tank? QUESTION As observed from the top of 150m tall light house the angles of depression of two ships approaching are 300 and 450. if one ship is directly behind the other, find the distance between the two ships. BACK LIGHT HOUSE 45 0 30 0 150 45 0 30 0 Problems with diagram A bridge across a river makes an angle of 450 with the river bank if the length of the bridge across the river is 150m, what is the width of the river ? DIAGR AM OF OBLEM THE PR 150 m 45 0 v Atree breaks due to the strom and the broken part bends so that the top of the tree touches the ground making an angle of 30 0 with the ground .the distance from the foot of the tree to the point where the top touches the ground is 10m . Find the height of the tree? vA Tower stands vertically on the ground. From a point on the ground, 20m away from the foot of the tower, the angle of the top of the tower is 60. what is the height of the tower ? vThe shadow of a tower ,standing on level ground, is found to be 45 m longer than when sun’s altitude is 30 0 than it was at 60 0. find the height of the tower?
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