WHOOO!!!! Bam! Ok, let's finish this problem. We have a right triangle and we are looking
for an acute angle in this triangle. Now I have given you all the sides three, four,
and five. So, you can use whatever trig function you like. We are going to use some kind of
trig function to find the angle measure of theta using any two of these three sides since
I have given you so much information about this triangle. How about we just use tangent.
We have the tangent of theta equals opposite over adjacent which is four-thirds. Now we
need to get that tangent function away from theta. If I said two times x equals ten, you
would do the inverse of multiplication which is divide both sides by two and get x equals
five. If I said you had x squared equals sixteen, you would do the inverse function of squaring
which is square root both sides and say that x is equal to plus or minus four. Well, if
I want to undo the tangent function I need to apply the inverse tangent to both sides
of the equation...(arctan) I am going to write, and this middle line may not be necessary
for your teacher, but I am going to apply the inverse tangent to both sides of this equation. I don't know
why I am working so hard to color code it. Inverse tangent of four-thirds. The tangent
function and the inverse tangent function will cancel out and that is why this is just
a teaching step. You don't necessarily need to show this for just doing right triangular
trigonometry, Theta is going to be the inverse tangent of 4/3. Now again, if you want your
answers to be in degrees please make sure that your calculator is in degree mode. The
little negative does stand for an inverse function. Two to the negative one is one half,
(2/3) to the negative one power is 3/2, so a lot of times we see these negative exponents
as just flipping the base or moving the base on which that negative exponent sits on. But,
when you talk about functions, this is an inverse math function. What do you put into
a trig function? An angle measure and you get out, as we can see, the sides of a triangle.
With an inverse trig function, you are putting in the sides of a triangle even if it is just
a decimal like one point three repeating. That decimal that does come from the ratio
or the division of two sides of a right triangle. So the inverse tangent of four-thirds, just
type that into your calculator hitting second or inverse or maybe control and then tangent
looking for that little negative one as an exponent, and type it into your calculator.
If you are in degree mode you are going to get theta is approximately equal to 53.13
degrees. That is how a trig function of sine, cosine, or tangent will allow you to find
the measurements of the acute angles in a right triangles. If you have one angle...
I was going to yell BAM! and get out of here but, if you have one acute angle and you are
totally confident that is correct you subtract that from 90 to find the other acute angle.
Inside a triangle you only have 180 degrees. So let's see 90 minus fifty is forty, forty
minus three is thirty-seven, and now we have 36.87 degrees. Now I am done... BAM!!! I am
Mr. Tarrou:D Go Do Your Homework! Thank you very much for watching and letting me help.
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