Q. 35.0( 4 Votes )

From the given figure, find the value of

(i) sin θ

(ii) tan θ

(iii) tan A – cot C


Answer :

(i) sin θ


We know that,



Side opposite to θ = BC = ?


Hypotenuse = AC = 13


Firstly we have to find the value of BC.


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


According to Pythagoras theorem,


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


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


(12)2 + (BC)2 = (13)2


144 + (BC)2 = 169


(BC)2 = 169–144


(BC)2 = 25


BC =25


BC =±5


But side BC can’t be negative. So, BC = 5


Now, BC = 5 and AC = 13


So,


(ii) tan θ


We know that,



Side opposite to θ = BC = 5


Side adjacent to θ = AB = 12


So,


(iii) tan A – cot C


We know that,



and



tan A


Here, θ = A


Side opposite to A = BC = 5


Side adjacent to A = AB = 12


So,


Cot C


Here, θ = C


Side adjacent to C = BC = 5


Side opposite to C = AB = 12


So,


So,


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