Question

What is the cosine ratio of angle PRQ?

Answer 1

The cosine of angle PRQ is 0.50043

Explanation:

From figure :

In triangle PRQ

angle RPQ = 90° - 60° = 30°

Angle PQR = 90°

SO, angle PRQ = 180° - ( 90° + 30° )

Or, angle PRQ = 60°

Now Cos ∠ PRQ =
`(QR)/(PR)`

I.e Cos 60° =
`(QR)/(PR)`

Now cos ∠ RPQ =
`(PQ)/(PR)`

Or, Cos 30° =
`(PQ)/(10)`

So, PQ = 10 × Cos 30°

Or, PQ = 8.66

Now QR =
`\sqrt{PR^(2)-PQ^(2)}`

Or, QR =
`\sqrt{10^(2)-8.66^(2)}`

So , QR = 5.00043

∵, Cos ∠ PRQ =
`(QR)/(PR)`

∴ Cos ∠ PRQ =
`(5.00043)/(10)`

I,e Cos ∠ PRQ = 0.50043

Hence The cosine of angle PRQ is 0.50043 Answer