Question

What is the measure of

Answer 1

40.1° (nearest tenth).

Explanation:

Sine Rule

`\boxed{\sf (\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)}`

where:

• A, B and C are the angles.
• a, b and c are the sides opposite the angles.

From inspection of the given diagram:

• n = PQ = 17 mm
• p = QN = 11 mm
• N = ∠QNP = 84.8°
• P = ∠NPQ

To find the measure of ∠NPQ, substitute the given values into the formula:

`\implies \sf (\sin N)/(n)=(\sin P)/(p)`

`\implies \sf (\sin (84.8^(\circ)))/(17)=(\sin (NPQ))/(11)`

`\implies \sf \sin (NPQ)=(11\sin (84.8^(\circ)))/(17)`

`\implies \sf \sin (NPQ)=0.644395787...`

`\implies \sf NPQ=\sin^(-1)(0.644395787...)`

`\implies \sf NPQ=40.1203887...^(\circ)`

Therefore, the measure of ∠NPQ is 40.1° (nearest tenth).