Answer to Question #148897 in Trigonometry for Leyon

Question

a ship leaves the port at 1am travelling north at the speed of 10 miles per hour At 4pm the ship adjusts its course 30 degrees westward. How far is the ship from the port at 5pm

Answer 1

Initial speed = 10 miles per hour

There are 15 hours between 1am and 4 pm

Final speed = 10*15 = 150 miles per hour

Using cosine rule:

x² = p² + q² - 2pqcos(180-@)

where @ = Angle theta

x² = 10² + 150² - 2(10)(150)cos(180^o - 30^o)

x² = 10² + 150² - 2(10)(150)cos 150^o

x = 158.74 miles