Aship sails from harbour h on a bearing of 084 for 340 km until it reaches point p. it the sails on a bearing of 210 for 160km until it reaches point q. calculate distance between point q and harbor. ( me find angle p, i do not know if i need to ise angle 210 to solve for qh)

QH = 227.8 km ≅ 228 km

Step-by-step explanation:

∵ The bearing from H to P is 084°

∵ The bearing from P to Q is 210°

∵ The distance from H to P = 340 km

∵ The distance from P to Q = 160 km

∴ The angle between 340 and 160 = 360 - 210 - (180 - 84) = 54°

( 180 - 84) ⇒ interior supplementary

By using cos Rule:

(QH)² = (PH)² + (PQ)² - 2(PH)(PQ)cos∠HPQ

(QH)² = 340² + 160² - 2(340)(160)cos(54) = 51904.965

∴ QH = 227.8 km ≅ 228 km

Angle at p is 54°

Distance between Q and harbor is

77249 km

Step-by-step explanation:

The bearing from H to P is 084°

∵ The bearing from P to Q is 210°

∵ The distance from H to P = 340 km

∵ The distance from P to Q = 160 km

∴ The angle at p = 84 - (210-180)

= 84 - 30

= 54°

Using cosine rule

And let's call length qh "x"

X = (hp)² + (pq)² -2(hp)(pq)cosx

X = 340²+160² -2(340)(160)cos54

X = 115600+25600 -2(54400)(0.587785)

X= 141200-63951

X = 77249km

in mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. there are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. the set of candidate solutions that satisfy all constraints is called the feasible set.

hoped i'm right lol