given that a=25 b=43 and c=17, solve triangle abc

Question

anonymous · Answer

attachment

campbell_st · Answer

so are they side measurements or angles measurements..?

anonymous · Answer

not sure thats all the question that its asking!!

campbell_st · Answer

so the letters in the question are all lower case..?

anonymous · Answer

oh ... it looks like this

campbell_st · Answer

ok... that makes more sense, you have been given 2 angles and 1 side

anonymous · Answer

oh

campbell_st · Answer

lets start with the easy one

if angle A = 25 and angle B = 43 what is the measure of angle C..?

anonymous · Answer

ummmm... i know im gonna sound dumb! but im not sure :(

campbell_st · Answer

here is a diagram

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campbell_st · Answer

ok... so the angles in a triangle add to 180 degrees

so C = 180 - 25 - 43

what would you say C is..?

anonymous · Answer

C=112

campbell_st · Answer

great... so you have eliminated 2 answer choices... its between A and B

so do you know the law of sines...?

anonymous · Answer

not really

campbell_st · Answer

you need the law of sines to find a and b

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campbell_st · Answer

wow... that makes it hard to answer the question

so the law of sines is uses the side and angle measures to find other sides and angles

the law you'll need is 

$$\frac{c}{\sin(C)} = \frac{a}{\sin(A)}$$ 

have you seen that before..?

anonymous · Answer

yea yea... but i dont remember a thing!

anonymous · Answer

i dont mean to sound mean or anything ! but im on timed test and i have 5 mins left... is it possible if you can help me faster ? thank you

campbell_st · Answer

ok... then here is a quick and dirty method to solve the problem... 

there is this stuff about triangles that says 

the longest side is opposite the largest angle 

the shortest side is opposite the smallest angle 

the middles length side is opposite the middle angle measure

so the angles in order of side are 

Angle C = 112             side c = 17 

Angle B = 43                side b = 12,5 or 7.5

Angle A = 25               side a  = 12.5 or 7.5 

so using the facts about sides and angles... what side matches angle A and which side matches angle A

campbell_st · Answer

think about the shortest is opposite the smallest angle

campbell_st · Answer

this quick an dirty method eliminates the need for calculations in this question

anonymous · Answer

so would the answer be B ??

campbell_st · Answer

that would be my guess

anonymous · Answer

alright... thank you very much campbell_st !