Yet another math problem (this one confuses me)

[Incis0r]

---

Members don't see this ad.

Hi all!

Sample question retrieved from a study material.

Freddy Rembrandy has just finished a modern painting on a canvass in the shape of a right triangle. The lengths of the two longest sides of the painting are 23 inches and 14 inches, and they meet at an angle of 55 degrees. Which expression can be used to determine the area of Freddy's masterpiece?

And then they give some answer choices.

But I'm having trouble with the question itself. If 23 and 14 are the longest sides, then 23 is the hypotenuse and 14 must be the side opposite the 55 degree angle right? Larger angles mean longer opposite sides. 23 is opposite the 90 degree angle, and the remaining two angles would be 55 and 35. If 14 is the next longest side, shouldn't it be opposite 55? Why is it adjacent to the 55 degree angle?

If 14 meets the hypotenuse at a 55 degree angle, then 14 is opposite a 35 degree angle, which suggests that there is a larger side opposite the 55 degree angle, but 14 is supposed to be the largest leg. Can you see my confusion? Is my understanding of the principles correct?

 

[FeralisExtremum]

If 23 and 14 are the longest sides, then 23 is the hypotenuse and 14 must be the side opposite the 55 degree angle right?

The question tells us that the 23 inch side and the 14 inch side meet at an angle of 55 degrees - therefore it is impossible for the 14 inch side to be opposite the 55 degree angle. It's adjacent to it.

 

[Incis0r]

The question tells us that the 23 inch side and the 14 inch side meet at an angle of 55 degrees - therefore it is impossible for the 14 inch side to be opposite the 55 degree angle. It's adjacent to it.

The question also tells us that 14 is the longest leg (since 23 and 14 are the longest sides and 23 is the hypotenuse). How can the longest leg be opposite the shortest angle? I just tried doing it that way, and I get the other leg to be 22.9, which makes the other leg longer than 14 and violates the premise of the question (14 is the longest leg).

 

[FeralisExtremum]

The question also tells us that 14 is the longest leg (since 23 and 14 are the longest sides and 23 is the hypotenuse). How can the longest leg be opposite the shortest angle? I just tried doing it that way, and I get the other leg to be 22.9, which makes the other leg longer than 14 and violates the premise of the question (14 is the longest leg).

Ok I see what you mean. If it's a right triangle, we know the angles must be 90, 55, and 35. But then the two longest sides should meet at the smallest angle, since it should be opposite the smallest side, but 55 is clearly not the smallest angle in the triangle. Your understanding of the principles is correct - I'll see if I can figure this out in the meantime.

 

[alexis2010]

Feralis is correct. If you solve for the third side you get 18.25 which opposite angle 55. side 14 is opposite angle 35.
I don't see where the confusion is here? how did you get 22.9??

 

[Incis0r]

Feralis is correct. If you solve for the third side you get 18.25 which opposite angle 55. side 14 is opposite angle 35.
I don't see where the confusion is here? how did you get 22.9??

Forget about the 22.9 for a second.

The confusion is in the problem- 14 is supposed to be the longest LEG since 23 and 14 are the longest sides (read problem text). The triangle is a right triangle, and the problem says that the side of 14 and the hypotenuse of 23 meet at an angle of 55 degrees. This implies the last remaining angle is 35. This is not possible because if the 14 and 23 meet at 55, then the 14 is opposite the 35 degree angle, which means that the side opposite 55 is larger than 14 (which you yourself calculated to be 18.25). This means that 18.25 and 23 are the largest sides, not 23 and 14- the confusion is that the problem text said 23 and 14 are the largest sides, so I was wondering how one could solve this: do I ignore the fact that the 14 is the second longest side ( problem text), or that they meet at 55 degrees (also in problem text) I posted here to confirm that I understood the principle (larger angle = larger opposite side) correctly since that is more important, which Feralis confirmed. Make sense?

 

[alexis2010]

Ohhhh I see what you are saying.