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, sin α = 4/5
(ii) cos α
We know that,
Here, θ = α
The side adjacent to angle α = PQ =3
Hypotenuse = PR =5
So, cos α = 3/5
(iii) tan α
We know that,
Here, θ = α
Side opposite to angle α = QR =4
Side adjacent to angle α = PQ =3
So, tan α = 4/3
(iv) sin β
We know that,
Here, θ = β
The side opposite to angle β = PQ =3
Hypotenuse = PR =5
So, sin β = 3/5
(v) cos β
We know that,
Here, θ = β
Side adjacent to angle β = QR =4
Hypotenuse = PR =5
So, cos β = 4/5
(vi) tan β
We know that,
Here, θ = β
Side opposite to angle β = PQ =3
Side adjacent to angle β = QR =4
So, tan β = 3/4.