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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

1 Answer

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Best 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, 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.

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