Q8 of 25 Page 9

The length of a string between a kite and a point on the ground is 90 meters. If the string makes an angle θ with the ground level such that tanθ =15/8, how high is the kite? Assume that there is no slack in the string.

Let AB be the height of kite.


Given:


To find: The length of AB.


Formula Used:




Explanation:



Let the height of string = “h” m



As we know,



In ΔPQR,



Perpendicular = PQ = 15


Base =QR = 8


According to Pythagoras theorem,


PR2 = PQ2 + QR2


⇒ PR2 = 152 + 82


⇒ PR2 = 225 + 64


⇒ PR2 = 289


⇒ PR = √289


⇒ PR = 17


As,



sin θ =


In ∆ABC,




17h = 90×15



⇒ 79.41 m


Therefore, length of string = 79.41 m.


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