Question

Find the length side

Answer 1

PR = 6.93 units

PQ = 13.86 units

Explanation:

From ΔPQR,

m∠Q = 30°

QR = 12

By applying tangent rule for the given angle in the triangle,

tan(30°) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

tan(30°) =
`(PR)/(QR)`

`(1)/(√(3))=(PR)/(12)`

PR =
`(12)/(√(3) )`

PR = 4√3 ≈ 6.93

Now we apply cosine rule,

cos(30°) =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

`(√(3) )/(2)=(QR)/(PQ)`

`(√(3) )/(2)=(12)/(PQ)`

PQ =
`(24)/(√(3) )`

PQ = 8√3 ≈ 13.86