Q. 65.0( 5 Votes )

In ∆PQR, Q is a right angle PQ = 3, QR = 4. If P=α and R=β, then find the values of

(i) sin α (ii) cos α

(iii) tan α (iv) sin β

(v) cos β (vi) tan β

Answer :


Given : PQ = 3, QR = 4


(PQ)2 + (QR)2 = (PR)2


(3)2 + (4)2 = (PR)2


9 + 16 = (PR)2


(PR)2 = 25


PR =25


PR =±5


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


(i) sin α


We know that,



Here, θ = α


The side opposite to angle α = QR =4


Hypotenuse = PR =5


So,


(ii) cos α


We know that,



Here, θ = α


The side adjacent to angle α = PQ =3


Hypotenuse = PR =5


So,


(iii) tan α


We know that,



Here, θ = α


Side opposite to angle α = QR =4


Side adjacent to angle α = PQ =3


So,


(iv) sin β


We know that,



Here, θ = β


The side opposite to angle β = PQ =3


Hypotenuse = PR =5


So,


(v) cos β


We know that,



Here, θ = β


Side adjacent to angle β = QR =4


Hypotenuse = PR =5


So,


(vi) tan β


We know that,



Here, θ = β


Side opposite to angle β = PQ =3


Side adjacent to angle β = QR =4


So,


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