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Given angle ABC with a=42, b=25, & A=94 correctly label the triangle & find the measure of angles B & C, and side c

An explanation of how to solve it would be very much appreciated!

Dec 11, 2019
edited by Roxettna  Dec 11, 2019

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For starters you have not labeled  the sides of your triangle properly.

Side a  must be  opposite angle A

Same for b and c

Always little anglers for sides and the Capital equivalent for the opposite angle.

After that you will need to use sine  rule to get another angles

and then angle sum of a triangle to get the third one.

You can display what you do for each step if you want. People will give you feedback.

Dec 11, 2019
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I got:

m angle B = 36.42       m angle C: 49.57          c = 32.05

B= sin^-1(25*sin(94)/42) = sin^-1 (0.593788125)

C= 180-(94+36.42628842490619) = 49.57...

c= 42/sin(94)*sin(49.57...) = 32.05

Roxettna  Dec 11, 2019
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Are you having a go at this one now Roxettna. ?

Dec 11, 2019
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Yes I am! I just took me a while to try it out. hopefully its right! :D

Roxettna  Dec 11, 2019
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All looks good to me.

The question does say to the nearest 10th.

It seems you are learning very quickly.  Good for you.

Just memorize those formulas.

Have you done that already or would you like some memory hints?

Melody  Dec 11, 2019
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Yes, I mostly struggle with memorizing them. If you have any tips, please let me know! I would greatly appreciate that!

Roxettna  Dec 12, 2019
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Well everyone hs there own methods for memorising things.

For these ones i would not worry too much about the letters as they change according to how a triangle is labeled.

You do have to be careful about labeling Angles with capital letters and the opposite side with the little letter equivalent.

The sine rule is just

Any side over the sine of its opposite angle, is equal to any other side over the sine of its opposit angle.

$$\frac{a}{SinA}=\frac{b}{SinB}=\frac{c}{Sin C}$$

The Cosine rule

I am discussing how it is used when you are looking for a side.

A lot of people would use a rearranged version  when they are looking for an angle

The cosine rule starts like pythagoras's theorum

The side you want squared^2 = the sum of the squares on the other 2 sides     eg   $$a^2=b^2+c^2$$

Then you take away 2* product of the sides you have * Cos (the angle opposite the one you have.

$$a^2=b^2+c^2-2bc\;cosA$$

That probably didn't sound that simple, so lets discuss it more.

The side letter at the front is the same as the angle letter at the end.

So you start with the side you want to find and end with the cos of its opposite angle    $$a^2= \dots\dots cosA$$

The beginning looks like pythagoras's theorum.     $$a^2=b^2+c^2\dots \dots cosA$$

then it is take away.. there is no more squares but we use the 2 again.  time the two sides that we know. -2bc

$$a^2=b^2+c^2-2bc\; cosA$$

EXAMPLE

Say your triangle was called PTR and you needed side PR

If you draw it you will see that side PR is opposite T  so you should rename it   t

The formula would be

$$t^2=p^2+r^2-2prCosT$$

Maybe that will help, maybe not, you decide :)

Melody  Dec 12, 2019
edited by Melody  Dec 12, 2019