# week 4 – math 10

This week we looked at trigonometry. Something new I learned was, how to draw a bearing and how to find a right triangle with that. First, to be able to do the question you must know how to draw a compass, Now that we can draw a compass we know how to solve the question easier. Next, we must know what a bearing means, Bearing: when making a complete turn or gradual turn, using a compass/degrees to measure the bearing (ex. used in turning planes and boats). Now that we know what a bearing is we can find out how to solve a question using a bearing.

Say for example, there was a question that asked a boat was heading direct north, then made a 200 degree bearing south, while travelling 60 km south then stopped. How far away are they from going directly south?

Well first we draw the compass the we start at the 0 degree/N and turn 200 degrees south, and draw a line of how far they travelled (60km) then connect it to the south line: Now, to find X we must first fins the missing angle which is done by 270 (because west is a bearing of 270) – 200 =  70. Now we take 90 – 70 = 20, because every quarter is 90 degrees. Now we know that our missing angle is 20 degrees.

Now we can find X, to find X we have to first label our triangle with Hyp (across from the right angle/90 degrees), Adj (beside the reference/given angle), Opp (opposite of the reference/given angle). So we can determine if it is cosine (adj/hyp), sine (opp/hyp), or tangent (opp/adj): Now we can write our equation, we know that X is opp, and the given side, 60 is Hyp, so that must mean we are using Sine/Sin of 20 degrees.

So our equation will be:

Sin 20 = X/60

Since X, is on the top of the fraction (where we want it), we now have to get X alone by moving the 60 over to the other side (by moving it must now multiply in stead of divide).

60(Sin 20) = X

Now we simplify and solve, rounding to the first decimal place.

20.5km = X

And that’s how you solve bearing questions! Hope it helped.