Trigonometric ratios –word problem
Now we are ask in this problem, in this challenge we actually workout the missing pronumeral
which is the angle down here in the ground I am going to read the question for you we
are going to read it together.
It is a tree 21 m tall as I said here it is.
Cast a shadow 29m long, that is a massive shadow there that is beautiful on hot summers
day.
What angle do the sun rise?
There is the sun coming down here make with the ground so this is the angle the pronumeral
thither that is what we are looking for.
Ok now the clues are in the question as you look at this question might ask yourself what
I have got?
Because that is the best question you can ask if you have a problem, “what have I
got?”
Look at this, what have I got?
Well I have got the height of 20 meters, I’ve got the shadow 29 meters and we have this
you seen a pronumeral we know it’s a right angle triangle because we are assuming it
is a flat ground.
So let’s write down now, what we want to find in the first step is to find which trig
ratio is it.
Now based on what we have, is it a sine, is it a cos or is it a tan, and if it is a tan
it is pretty much hard to get if you are in the shade, but it could be a tan just check
this out.
We have, first of all a front from a thither going directly opposite right here 21 meters
so what’s that going to be obviously – opposite, that is a part of trig ratio and then right
next to it because the angle is attached to the ground right here is the 29 meters, what
is that going to be right next to it?
It’s called a did you know – it is the adjacent isn’t it?
So we have opposite over adjacent let’s write that up – now we which of the three
ratio, is it sine, cos or tan?
Tan I hear from you – so let’s put that in the good news – so that is tan, tan – thither
equals opposite over adjacent which equals what numbers do we have – we have to ask
that question again – what have I got?
Looking at the diagram I have the opposite right across here 21 meters let’s put that
in – all over adjacent right down here in the shadow 29 meters – okay cool.
Now let’s continue, let’s go tan thither – equals – now on the calculator I like
to turn into decimal but if you prefer to keep it as a fraction that’s fine – 21
divided by 29 as a decimal is 0.724 – let’s write that in – okay, 0.724 - okay, now
I want to get the thither by itself right here so let’s put that here - now the way
to do that is reimburse the tan both side or shift tan if you prefer, so that means
we have on the right hand side now – tan inverse that would give a negative one power
to shift to inverse and then we have 0.724 in there – now we can put that in the calculator
so shift tan or second function tan 0.724 and that would yield into decimal degree.
So thither equals putting that in there – 35.9097 degrees, that is a decimal degree that’s
not a minutes and seconds it’s a decimal degree.
35.9097 degrees now let’s change it into degrees minute seconds, well put that in the
calculator again, shift dms or shift you know the those 2 thither add the degrees minutes
seconds and you will get 35 degrees 54 minutes and the seconds are right in blue, the seconds
is 35 seconds, now let’s take a look, do we climb up or do we stay down?
This is the big question – we have 54 minutes let’s get up to the newest minute – now
54, 35 notice that 35 is above thirty and when it’s above thirty what we are going
to do with the minutes?
We go up, so therefore the nearest minute the answer for that angle in the ground the
sun is rise coming down is – 35 degrees and 55 minutes.
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