Answer:
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
Answer:
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
