PLZZZZ TRIG QUESTION I NEED IT ROGHT NOW?

Question

a plane leaves the airport and travels due north for 230km. It than changes courses and travels N40* (bearing of 40*) for 350km how far is the plane from the airport a digram would he lot to plz

Answer 1

Plane traveled distance in north direction n = 230 km

Plane traveled distance in bearing of 40° north direction b = 350 km

Angle of Plane changed direction to north θ = 40°

Distance from the airport to the present position of plane d = ?

Using the Cosine rule : d² = n² + b² - 2nb cosθ

d² = 230² + 350² - 2(230)(350)cos(180-40)

d² = 52900 + 122500  - 161000 cos140

d² = 175400 - (-123333.1553)

d² = 298733.1553

d = √298733.1553 = 546.565 km

Solution : Distance from the airport to the present position of plane is 546.565 km