Triangle problems

[Loki123]

The triangle of the radius of the circle R = 7sqrt (3) / 2, the difference of the sides a and b is equal to 5 and the side c = 7, rotates around the longest side. Calculate the area and volume of the resulting body.

My thought process was like this, I need to determine the longest side so I can even attempt to calculate volume and area of the resulting body. I got c, I have no idea how to get a and b. How do I do this?

 

[lev888]

The triangle of the radius of the circle

???

 

[Dr.Peterson]

The triangle of the radius of the circle R = 7sqrt (3) / 2, the difference of the sides a and b is equal to 5 and the side c = 7, rotates around the longest side. Calculate the area and volume of the resulting body.

My thought process was like this, I need to determine the longest side so I can even attempt to calculate volume and area of the resulting body. I got c, I have no idea how to get a and b. How do I do this? View attachment 30807

You mean R is the circumradius of the triangle, right?

Is [imath]a-b=5[/imath], or [imath]3[/imath] as in the image?

How do you conclude that [imath]\gamma=60^\circ[/imath]? (I assume [imath]\gamma[/imath] is the angle between a and b.)

 

[blamocur]

The triangle of the radius of the circle R = 7sqrt (3) / 2, the difference of the sides a and b is equal to 5 and the side c = 7, rotates around the longest side. Calculate the area and volume of the resulting body.

My thought process was like this, I need to determine the longest side so I can even attempt to calculate volume and area of the resulting body. I got c, I have no idea how to get a and b. How do I do this? View attachment 30807

This is quite confusing: first you say that a-b=5, then you switch to a-b=3. Same with R: from [imath]\frac{7\sqrt{3}}{2}[/imath] to [imath]\frac{7\sqrt{3}}{3}[/imath].

 

[Dr.Peterson]

I have no idea how to get a and b. How do I do this?

Have you tried the Law of Cosines? Assuming the hand-written version of the problem is correct, this gives nice numbers.

 

[Loki123]

Have you tried the Law of Cosines? Assuming the hand-written version of the problem is correct, this gives nice numbers.

I just tried it and it works. Sorry for the mistakes. There were two similar problems, I was solving the second one but posted the text of the first one... In my defense I was very tired.