Q. 4 A3.9( 36 Votes )

In ∆ABC, right angled at B, AB = 24 cm, BC = 7 cm. Determine

a. sin A, cos A

b. sin C, cos C

Answer :


(i)


(a) sin A


We know that,



So, here θ = A


Side opposite to A = BC = 7


Hypotenuse = AC = ?


Firstly we have to find the value of AC.


So, we can find the value of AC with the help of Pythagoras theorem.


According to Pythagoras theorem,


(Hypotenuse)2 = (Base)2 + (Perpendicular)2


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


(24)2 + (7)2 = (AC)2


576 + 49 = (AC)2


(AC)2 = 625


AC =625


AC =±25


But side AC can’t be negative. So, AC = 25cm


Now, BC = 7 and AC = 25


So,


Cos A


We know that,



So, here θ = A


Side adjacent to A = AB = 24


Hypotenuse = AC = 25


So,


(b) sin C


We know that,



So, here θ = C


The side opposite to C = AB = 24


Hypotenuse = AC = 25


So,


Cos C


We know that,



So, here θ = C


Side adjacent to C = BC = 7


Hypotenuse = AC = 25


So,


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