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
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