Question

A boat in calm seas travels in a straight line and ends the trip 22 km west and 53 km north of its original position. To the nearest tenth of a degree, find the direction of the trip

Answer 1

Okay, let's view the object's path rather than just a straight line as two vectors that together form the hypotenuse of a triangle, like this:

Answer 2

That being said, what they're looking for is the angle from the normal, which would be the angle between the hypotenuse of the triangle and the side that's 53 kilometers north. In order to find this, let's use trigonometry. Do you know what SOHCATOA means?

Answer 3

no

Answer 4

Okay, do you know about Sine, Cosine and Tangent and what they are? All of these are essentially ratios between the lengths of triangle sides. Sine is the ratio between the Opposite side to an angle and the Hypotenuse of a triangle (Sine=(Opposite/Hypotenuse), hence, SOH.) The Cosine is the ratio between the adjacent side to the hypotenuse (Cosine=(Adjacent/Hypotenuse), hence, CAH), and the Tangent is the ratio between the Opposite and Adjacent sides, (Tangent=(Opposite/Adjacent), henca, TOA). SOH-CAH-TOA.

Answer 5

If you manipulate these ratios, you can find the actual degree value for that angle. So let's first look for some ratio we can use to get the angle we're looking for, which in this situation would be the tangent: