a ship leave port p and sails on a bearing N50 degree E to Port Q 15km away. then it sails on a bearing of S45 degree E to Port R, 20km away

Port r is 100° from Port p and 26km from Port p

Step-by-step explanation:

Lets note the dimension.

From p to q = 15 km = a

From q to r = 20 km = b

Angle at q = 50° + 45°

Angle at q = 95°

Ley the unknown distance be x

Distance from p to r is the unknown.

The formula to be applied is

X² = a² + b² - 2abcosx

X² = 15² + 20² - 2 (15) (20) cos95

X² = 225+400 - (-52.29)

X² = 677.29

X = 26.02

X is approximately 26 km

To know it's direction from p

20/sin p = 26/sin 95

Sin p = 20/26 * sin 95

Sin p = 0.7663

P = 50°

So port r is (50+50) ° from Port p

And 26 km far from p