Hi guys I have over here a practical example with angles, that angles is right here we
have this lady name Jackie and she is in this boat and she is go on sailing on this beautiful
Sunday afternoon and she is laughing it up and basking in the sun and she notice this
cliff, why out here?
500m out from where she is, so she get a little protect her out and actually measures the
angle of elevation.
What is the angle of elevation from the horizontal or the main sea level upwards to the target
of your measurements.
Which in this case this is the top of a cliff so she is aiming to right to the edge, right
to the a peaks of the that cliff.
So she measure 32 degrees 15 minutes so the good news about trigonometry is this tool
allows you to measure height of objects whether be building, cliff, hill, mountains easily
without having to physically measure it all you need to know is how far you are and the
angle of elevation that is all you need is in that terrific.
Well let us do that now, let us work out the height or H of this cliff, so what are the
steps?
First of all we need to do is to determine what ratios is it?
for example sin, cos or tan?
Then we plunk it in to trig ratio and we put in the 500, and 32 15 and we can come up with
the height the height of the cliff.
Now the good news is we do not need to give in centimeter or milliliter all they want
it is in the nearest meter.
Let us do that let us round it up in the nearest meter so let us decide where that angle is
going to?
So I am looking at this and Jackie is in the boat and it is a bit bumpy here and she is
kind a protected there and that is 32 degrees 15 she measures and she is look directly in
front of her and clearly is what?
It is the opposite, yeah?
And the other measurement is the 500m how far she is from the base of the cliff to the
boat?
And that is already measured and that happens to be the right of the angle, yeah?
of is the angle of elevation and it is called ADJ, yeah that is adjacent which means right
next to it.
so we have established that is always the first thing let us write that up over adjacent
now by now you probably know what opposite over adjacent is, what is it?
yes it is a tan that is right, tan theta = opp /adj and that equals let us put in the numbers.
Well straight over here for the opposite we have H let us put that in all over adjacent
which is the distance from boat all the way base of the cliff we can see here written
there 500 m let us put that in – Ok now what we need to do is, I guess what
we want to do is multiply both sides by 500 so we left with the H by itself, so I am going
to multiply by 500, x by 500, x by 500 why?
Because we are looking for H we want that H —all by itself . so it is going to be
500 x tan ( what is tan again?
32 degrees 15 minutes) – 32 degrees 15 minutes ok, and that is going to equal as you can
see the H there let us bring the H which is the height of the cliff.
Now what I might like to do is work out what tan 32 degrees 15 let us go through the calculator
process and sequence here.
now 32 15 how are we going to do the tan on that?
What we are going to do, go tan 32 degrees but when you put the 32 , we got the 32 dms
( or degreed minutes seconds) and then we press 15 dms and that will change into degrees
minutes seconds so the calculator can process it so then we end up with 500 x 32 15 ( once
you put in your calculator is going to yield) 0.631 ok, and that is going to equal of course
our height which is what we are looking for.
Height of we cliff so we just put in 500 x 0.631 the height of that cliff yields – h
= 315.47 that is what the calculator says round it up now the 4 is lower so that means
we can go to the final answer h =, and this is the height of the hill to the nearest meter
315m.
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