Answer:
The cosine of angle PRQ is 0.50043
Step-by-step 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 = [tex]\frac{QR}{PR}[/tex]
I.e Cos 60° = [tex]\frac{QR}{PR}[/tex]
Now cos ∠ RPQ = [tex]\frac{PQ}{PR}[/tex]
Or, Cos 30° = [tex]\frac{PQ}{10}[/tex]
So, PQ = 10 × Cos 30°
Or, PQ = 8.66
Now QR = [tex]\sqrt{PR^{2}-PQ^{2}}[/tex]
Or, QR = [tex]\sqrt{10^{2}-8.66^{2}}[/tex]
So , QR = 5.00043
∵, Cos ∠ PRQ = [tex]\frac{QR}{PR}[/tex]
∴ Cos ∠ PRQ = [tex]\frac{5.00043}{10}[/tex]
I,e Cos ∠ PRQ = 0.50043
Hence The cosine of angle PRQ is 0.50043 Answer
