Hi guys in this example we are looking the angle, which angle?
The missing angle right up here in yellow theta (t-h-e-t-a) it is like an O with a line
through it . Now with this theta we are in a right angle triangle so that means we can
use the trig ratio sin, cos or tan.
What are we given?
Let us have a look at the clues in this question we have the 6 across here and we have this
long length down here the distance is 17 so our task and mission is to work out the theta.
The first step that we are going to do is to work out the trig ratio substitute it in
there and then once we discover which ratios it is sin, cos or perhaps tan?
As we work it out then we are going to get the answer an inverse or shift the sin, the
cos, or the tan shift it and come up with an answer when we are going to have degrees,
decimal degrees and then we are going to change to degrees into degrees minutes seconds there
is a function in your calculator, that turn shift degrees minutes seconds and it will
turn into what you want, degrees minutes seconds and then we are going to round it up to the
nearest minutes why?
Because we have 60 seconds in a minute and 60 minutes in one degree we are not talking
about time 60 minutes in an hour, we are talking about degrees so degrees are broken in to
what?
Degrees minutes seconds in this seconds are going to take in this example round them up
into minutes so let us do this example.
First thing is to get the ratio let us write it up now, well there is the theta we are
looking for – and the ratio will be, let us have a look at that 6 there that is what
is given to us.
We are about is that 6 have a look at the right next to it, right next is theta it start
with A what is it?
ADJ it is adjacent and right here is long lengths you have probably already know that
is HYP for long length or distance on a triangle is the hypotenuse so let us write those ratios
out.
so theta = adjacent – over hypotenuse.
Okay, now, let us work out.
Adjacent of the hypotenuse is it a sin?
No. it is a tan?
No. it is a cos, let us put on the cos in there.
Cos theta = adjacent over hypotenuse and what is thus that equal?
It is 6/17 as we can see so let us write it down, 6 over 17.
Now let us change this down here, let us bring it down there.
So we can say, cos theta = now 6 divided by 17 on the calculator will give you a decimal.
I like working with decimal, some people like to live as fraction form in the calculator
you are welcome to do either way either option works I prefer decimal in this example I am
going to do decimals 6/17 gives you a decimal of 0.353 rounded up to three decimals places.
Now what we are going to do is get this theta all by itself individually so let us do that.
So the way to do that is shift cos, inverse cos or second function cos depending on the
calculator and bring the cos over that side and the theta becomes and individual by itself.
So that = cos power minus 1 means shift or inverse, bracket 0.353 – 0.353 cool.
Now let us go to the calculator again and on the calculator, shifting cos 0.353 push
the buttons in there you will yield your answer in the decimal form, so you will be degree
in decimal form.
So that would be whole degrees of 69 degrees point 3327 and you can also put the degree
here if you wish so 69.3327 there are no degrees, minutes, or seconds yet, so that is what we
are going to do know.
So let us do that, so w are going shift degrees, minutes, seconds will give you degrees, minutes,
seconds by pressing that button and you will end up with 69 degrees 19 minutes and 57 seconds.
This is what I was talking about earlier.
Now how do we round up or round down, well when we are talking about degrees and minutes
and seconds when they are above 30 we round the minutes up by 1, so that is when above
30, when below 30 we keep the minutes are they are , in this situation is in it true
that we have seconds they are above 30 that is right it is true it is 57 that is way above
30 so this 19 will round up so the angle the missing theta is, theta = 69 degrees that
is rounded up so that becomes 20 minutes and that is the answer the missing pro numeral
theta right over there.
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