## pythagoras123 one year ago In a triangle ABC, the ratios of the sides are such that a:b:c = 2:3:4. Calculate the value of cos C and hence find the value of sin C.

1. triciaal

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2. triciaal

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3. pythagoras123

uh could you show how you calculate sin C using the above formulas

4. pythagoras123

@triciaal

5. triciaal

given only the 3 sides of the triangle first use the cosine rule to find the largest angle ( the one opposite the longest side) then you can use the sine rule to find the other 2 angles. Here we only need to find the sin of c we already calculated C you just use the calculator to find sin C.

6. pythagoras123

oh my question requires it to be in exact form

7. pythagoras123

is there a way to find sin C without the calculator

8. triciaal

@jim_thompson5910 @ganeshie8 can we use the ratio of the sides of the triangle as the lengths of each side?

9. triciaal

@pythagoras123 use the Sin rule above

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@Nnesha @zepdrix what would be the lengths of the sides for this triangle?

11. pythagoras123

@triciaal we don't know any of the values for sin A, sin B or sin C

12. triciaal

not until after we find the largest angle. you need to read the responses more carefully.

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15. pythagoras123

I get that but how do we use the value of cos C to find the value of sin C without solving for the angle C itself?

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17. pythagoras123

oh I get it now lol thx

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19. pythagoras123

so with just the ratios of the sides given, we can find the trig ratio?

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21. pythagoras123

ok thx for your help :)

22. triciaal

cosine rule C is the largest angle

23. triciaal

you are welcome

24. triciaal

@zepdrix thanks