I'm forgetting my geometry. Can I solve this triangle?

[dzidziaud]

Homework Statement

So I'm doing a physics problem, and I think I'd get the right answer if I solved this triangle. I don't know any angles. The base is 56 meters long, its height is 500 meters, and the difference between the other two sides is 4 meters. Can I figure out the sides based on this information?
If not, can I at least find out the difference in position of the vertex between the two unknown sides if they were equal vs in this situation? I hope that makes sense.

 

[Chestermiller]

Homework Statement

So I'm doing a physics problem, and I think I'd get the right answer if I solved this triangle. I don't know any angles. The base is 56 meters long, its height is 500 meters, and the difference between the other two sides is 4 meters. Can I figure out the sides based on this information?
If not, can I at least find out the difference in position of the vertex between the two unknown sides if they were equal vs in this situation? I hope that makes sense.

Yes. You have enough information to figure out the sides. Think Pythagorean Theorem.

Chet

 

[dzidziaud]

Yes. You have enough information to figure out the sides. Think Pythagorean Theorem.

Chet

I am assuming you mean by dropping a perpendicular that is the height of the triangle, so it is split into two right triangles? I can't figure out what to do from there though because I don't know how the 52 m side is split.

 

[Chestermiller]

I am assuming you mean by dropping a perpendicular that is the height of the triangle, so it is split into two right triangles? I can't figure out what to do from there though because I don't know how the 52 m side is split.

Split it into y and 56-y, and then get two equations in two unknowns. Of course, the other two sides are x and x+4.

Chet

 

[dzidziaud]

Thanks, I finally figured it out! Unfortunately, I got the wrong answer, so I'm approaching the actual physics problem wrong. At least I got some good geometry practice out of it :)