How Do You Calculate the Distance and Speed of a Boat Using Trigonometry?

[Hurly]

Homework Statement

Amateur astronomers often approximate angles with an arm out-
stretched. With the hand in this position, one finger's width is approximately
2 degrees, the width of your hand at the knuckles is approximately 10 degrees, and your
hand fully spanned is approximately 20 degrees,. You are on the shore and you see a
boat. With your arm outstretched, the height of its mast is 1 finger's width.
You also know that this boat's mast is 10 metres in height. How far away
is the boat? 30 seconds later you notice the mast is now 2 finger widths in
height. How fast is the boat sailing towards you? Now convert this speed
into knots (look it up).

Homework Equations

1 fingers = 2 degrees,

The Attempt at a Solution

I don't know where to start

 

[scurty]

Drawing a picture for these types of problems is handy. Reread the beginning of the problem where it lists how many angles each of the parts of the hand is and write them down. Then go through the problem and try to draw everything that is being described.

The hard part in word problems is setting up the problem in equation form. It is usually simple and straight forward after that.

 

[HallsofIvy]

You need to know some basic trigonometry for this problem- in particular that \tan(\theta)= "opposite side divided by near side". A quick sketch of the problem should show you that the "opposite side" is the mast and the "near side" is the distance to the boat.