the sides of a triangle measures 13.4 centimeters, 18.7 centimeters, and 35.6 centimeters. Find the measure of the angle with the least measure. round to the nearest tenths of a degree

Question

anonymous · Answer

@Zarkon  can u help me with this

mathstudent55 · Answer

Can you tell which angle has the smallest measure? The one opposite which side?

mathstudent55 · Answer

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anonymous · Answer

C has the smallest

anonymous · Answer

@mathstudent55

anonymous · Answer

Use the law of Cosines
$$

a^2= b^2 +c^2 - 2 bc \cos(\theta)
$$

anonymous · Answer

The smallest angle is the one opposite to the smallest side. In our case, it is the one opposite to 13.4

anonymous · Answer

so do i plugin 13.4 for c then @eliassaab

mathstudent55 · Answer

Right. C is the smallest angle because it's opposite the smallest side.

Now use the law of cosines written in a way that you have $ \cos C$ as an unknown and the lengths of the sides as known quantities.

anonymous · Answer

$$
13.4^2=18.7^2+35.6^2 -2 (18.7 )(35.6) \cos (\theta )
$$

anonymous · Answer

@wolf1728  over here

anonymous · Answer

Find $ \large \cos(\theta) $ then find $ \large \theta $

anonymous · Answer

There is no triangle with these three sides. Why?

mathstudent55 · Answer

$c^2 = a^2 + b^2 - 2ab \cos C$

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anonymous · Answer

$$
13.4 < 35.6-18.7 = 16.9
$$

anonymous · Answer

Each side of a triangle must be bigger than the difference of the other  2 sides

anonymous · Answer

i got -1437.49=-1331.44cos c ???

mathstudent55 · Answer

@eliassaab is correct. Since the length of one side, 35.6, is greater than the sum of the other two lengths, there is no triangle with these side lengths.

anonymous · Answer

If you try to solve it you find 
$$
\cos (\theta )=1.07965
$$
whic is impossible

anonymous · Answer

sorry about that guy i messed up it actualy 13.4,18.7, and 26.5 lol my bad guys

wolf1728 · Answer

Yes, that's right - the triangle cannot be formed with sides of those lengths.

anonymous · Answer

You should be able to do it on your own now.

anonymous · Answer

im not sure can u walk my through it @eliassaab

anonymous · Answer

I will let @mathstudents55 guide you tru it

mathstudent55 · Answer

$13.4^2=18.7^2+35.6^2 -2 (18.7 )(35.6) \cos C$

$179.56 = 349.69 + 1267.36 - 1331.44 \cos C$

$-1.07965 = \cos C$

This is impossible because $ -1 \le \cos \theta \le 1$.
The range of the cosine function is from -1 to 1, inclusive.
The cosine of an angle cannot be equal to -1.07965, so there is no triangle with these side lengths.

anonymous · Answer

yea i know @mathstudent55 check my last comment

anonymous · Answer

so the answer is 28.3 @wolf1728

anonymous · Answer

as the smallest angle

mathstudent55 · Answer

No. The answer is that there is no triangle with these given side lengths, so there cannot be any angles.

mathstudent55 · Answer

|dw:1387828595000:dw|

anonymous · Answer

did u check my comment correcting my self @mathstudent55

mathstudent55 · Answer

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mathstudent55 · Answer

I saw it now.
Let me do it again using the corrected sides lengths.

anonymous · Answer

i got the answer its 28.3

mathstudent55 · Answer

Correct.