I'm not sure if the answer I have below is correct because I'm pretty sure you wouldn't need to know this formula for the gre's:

3:5:7 = a:b:c

angle(C) = arccos ( (a^2 + b^2 - c^2) / (2*a*b) ) = arccos( (9 + 25 - 49) / (30)) = arcos(-1/2) = 120

However, this would lead to the correct choice A. Does anyone know an easier way to get this answer (and, is the equation I have above correct? Just curious)

Thanks

The way you solved is not forbidden on the GRE. However, it not necessary derivatives or else

Thanks for the response. Looking at your answer, are you saying the angle has to be a multiple of the 3 ratios, and in this case, the answer is 105 not 120? Sorry, I guess I just wasn't familiar with the approach you took, but would like to know it.

Thanks

mmmmmhhhh

something is wrong here at a closer look

If we use the unknown multiplier based on the ratio

we do have that 3x+5x+7x=180 (the sum of all angles in a triangle)

15x=180

x=12

7*12=84

The largest angle must be 84 and the answer is C and NOT A

I edit the OA accordingly

Hello,

At first, I thought this would've worked as well, using the same ratio for angles. But I think this only works for an equilateral triangle?

Just to give a quick example, using a right triangle with two equal angles we'd have the ratio of angles equal to 45:45:90, or 1:1:2. But the sides wouldn't have the same relationship because by rule, the sides would have the ratio of 1:1:\sqrt{2}. So technically, I don't think you could apply the ratio for sides to angles?

Thanks again for the responses. Thought this was an interesting question. Maybe knowing that the angles ratio deviates more than the sides ratio is enough to answer the question (as in, knowing that the largest angle is greater relative to the other angles compared to the largest side relative to other sides would be enough to know this angle > 84 deg)

The unknown multiplier when you do have a ration works for any type of triangle

The question has given the information that the ratio of the length of 3 sides are 3,5,7. How can we use the length of the sides to determine the respective angles? you've multiplied these ratios with a constant and made it equal to 180, but these are the ratio of lengths not the ratio of angles! I'm so confused here

Can someone explain the answer because i don't get that why did they took the sides ratio for sum of all angles in the triangle which is 180.