Q. 7 A

If then find the values of cos θ and tan θ.

Answer :

Given:



We know that,



Or



Let,


Perpendicular =AB =4k


and Hypotenuse =AC =5k


where, k is any positive integer


So, by Pythagoras theorem, we can find the third side of a triangle


In right angled ABC, we have


(AB)2 + (BC)2 = (AC)2


(4k)2 + (BC)2 = (5k)2


16k2 + (BC)2 = 25k2


(BC)2 = 25 k2 –16 k2


(BC)2 = 9 k2


BC =9 k2


BC =±3k


But side BC can’t be negative. So, BC = 3k


Now, we have to find the value of cos θ and tan θ


We know that,



The side adjacent to angle θ or base = BC =3k


Hypotenuse = AC =5k


So,


Now,


We know that,


Perpendicular = AB =4k


Base = BC =3k


So,


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