Geometry problem

[Hakoda]

I'm just finishing up some physics homework for the summer. Teacher gave us some geometry and algebra review to refresh our memories as summer hw.

Below is a problem that she's given us and I seem to be somewhat ambivalent towards what I think the answer is.

The question is to simply solve for the angle measure of theta. Is it correct to assume the triangle above the theta symbol is a right triangle?

Could someone please fix that title.

 

[SinHarvest24]

I'm gonna make a guess here and say that the answer is 30o.

 

[chris888222]

Personally I don't think it is right to assume. I always have the same mistake with vertically opposite angles when I assume they are (the question didn't state, so...)

Wait, is the theta triangle inside a square/rectangle? If yes then yup it's a right triangle

 

[Hakoda]

I'm gonna make a guess here and say that the answer is 30o.

That's what I thought as well. I came to this conclusion by seeing that the smaller triangle (between the straight line & the giant 30) is similar to larger one. This means that the angle near the bottom-right of the square is 60o. If this is 60o the corresponding angle, (located inside the smallest triangle above the theta symbol) is also 60o and then theta is 30o.

@Chris, Yes that's the one. I'm only asking because it doesn't indicate the slanted line is perpendicular to the square's base.

 

[Maz7006]

I remember taking this crap in mechanics during freshman

the angle theta is 30 degress; the proof is quite long, didn't think they'd actually give you this is school, and i dnt remember it exactly, but i always remember that with ever such problems with an incline, the unknown angle (in its given position) is the same as the known one to the right on the right angle triangle in which the object is on - if that makes any sense.

 

[Nathan Drake]

That base triangle is likely a 30, 60, 90 triangle. It is one of the basic ones that I learned about in pre-calculus. The other basic triangle is 45, 45, 90.

Regardless, I believe that is a 45, 45, 90 triangle inside of it, so I want to go with theta being a 45 degree angle.

Mostly a guess mind you.

 

[mcp2]

Am I safe in assuming that the box is resting on a slope of angle 30 degrees?

 

[The Pi]

First of, the question does not contain suitable information to produce an answer.

However I you assume that the line that cuts the hypotenuse is perpendicular the answer is 30 degrees.

Complete the large triangle, the other angle is 60.
Opposite angle to that 60 is 60.
Now here's the issue, you don't know if the line that cuts the hypotenuse is perpendicular if it is, complete the small triangle, the last angle is 30 which is the answer.

 

[Nathan Drake]

And thus, I have been proven to be as bad with triangles as I thought. Damn you geometry. I only passed because I didn't have to work.