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OpenStudy (anonymous):

In triangle ABC, the ratio of the angle is A:B:C=2:3:4. What is the measure of the smallest angle?

OpenStudy (amistre64):

the smallest angle is opposite the shortest side

OpenStudy (amistre64):

and we can calculate that angle using a modifies law of cosines

OpenStudy (amistre64):

\[cos^{-1}\left(\frac{short^2 - side^2-other.side^2}{-2(side)(other.side)}\right)=angle\]

OpenStudy (amistre64):

\[cos^{-1}(\frac{2^2 -3^3-4^2}{-2(3)(4)})=angle\] \[cos^{-1}(\frac{4 -9-16}{-24})=angle\] \[cos^{-1}(\frac{11}{24})=angle\]

OpenStudy (amistre64):

helps to know how to add... let me fix that

OpenStudy (amistre64):

\[cos^{-1}(\frac{21}{24})=abt.\ .5054^o\]

OpenStudy (anonymous):

um thats not any of the choices (1)20 (2)40 (3)60 (4)80

OpenStudy (amistre64):

may calc was on radians :)

OpenStudy (amistre64):

OpenStudy (amistre64):

\[2^2 = 3^2 + 4^2 -2(3)(4)\ cos(a)\] \[4 = 9 + 16 -24\ cos(a)\] \[4-9-16 = -24\ cos(a)\] \[-21/-24 = cos(a)\] \[cos^{-1}(21/24) = a\] or at least it should right?

OpenStudy (amistre64):

that equals about 30 degrees

OpenStudy (amistre64):

but thats aint a choice is it

OpenStudy (anonymous):

nope

OpenStudy (amistre64):

the next biggest one = 9-4-16 11 ------- = ---- ; cos-1(11/16) = abt 47 degrees -2(2)(4) 16 30 + 47 = 77 180 -77 ---- 103

OpenStudy (amistre64):

those are the answers; but your choices are either mistyped, or someone messed it up in the program :)

OpenStudy (anonymous):

lol its a prep regent

OpenStudy (amistre64):

28.955 degrees is the smallest angle tho ;) good luck with it

OpenStudy (anonymous):

lol thanks for trying

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