Math destroyer practice test 5 #26

[sprint2k]

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Is there a reason why the bottom triangle should be 30-60-90?

It's been a while, and i'm not too familiar with identities.

 

[sacapuntas]

Since I believe X is supposed to be parallel to the top triangle side that has the 90 and theta on it, and you are given the angle of 30 degrees on the bottom triangle, you can know that you have a 90 degree and a 30 degree on both triangles leaving a 60 degree. Sorry if this isn't clear, I don't have time to add to arrows to your picture to show what angles I am talking about.

Is there a reason why the bottom triangle should be 30-60-90?

It's been a while, and i'm not too familiar with identities.

 

[EyEnStein 07]

Yes, look up alternate interior angles. All angles of a triangle sum to 180 degrees. Its should be obvious which side on the bottom triangle is 90 degrees.

The angle on the top triangle that is NOT THETA is also 30 degrees, because its "alternate and interior" to the 30 degree on the bottom triangle.

180-90-30 = 60 left for theta.

If you need the sides you could have either memorized that the side ratios (i think its 1:sqrt(2):2 (hyp) but I'm not sure , double check). The other way to do it is by saying that (looking at the top triangle):

sin(60) = x/5 ---> x = ??
cos(60) = y/5 ---> y = ??

 

[sprint2k]

i still don't understand. it's not given that x is parallel to the right side. if that were the case, it would be mentioned right? or the supposed 90 degree angle of the lower triangle would be marked 90 like the top one has?

my question is. why is it: 30 60 90:, why isn't is :30, 65, 85" or "30, 55, 95"

 

[sprint2k]

Yes, look up alternate interior angles. All angles of a triangle sum to 180 degrees. Its should be obvious which side on the bottom triangle is 90 degrees.

The angle on the top triangle that is NOT THETA is also 30 degrees, because its "alternate and interior" to the 30 degree on the bottom triangle.

180-90-30 = 60 left for theta.

If you need the sides you could have either memorized that the side ratios (i think its 1:sqrt(2):2 (hyp) but I'm not sure , double check). The other way to do it is by saying that (looking at the top triangle):

sin(60) = x/5 ---> x = ??
cos(60) = y/5 ---> y = ??

for the top triangle, the angle that is not theta is not 30 degrees. i'm pretty sure the slanted lines are not parallel as you can't assume anything and it's not given. unless there is some identity of that picture i don't know about, the picture is literally the only information that is given.

 

[sacapuntas]

for the top triangle, the angle that is not theta is not 30 degrees. i'm pretty sure the slanted lines are not parallel as you can't assume anything and it's not given. unless there is some identity of that picture i don't know about, the picture is literally the only information that is given.

How do you know theta is not 60 and the other angle on top is not 30 degrees?

 

[sprint2k]

How do you know theta is not 60 and the other angle on top is not 30 degrees?

that's what i'm asking

how do you know that it is? it's not given. the picture is literally all that is given. can you conclude that the top triangle's theta = 60 by just the picture?

 

[sacapuntas]

that's what i'm asking

how do you know that it is? it's not given. the picture is literally all that is given. can you conclude that the top triangle's theta = 60 by just the picture?

Yes, you can. I looked in my math destroyer and the picture does not have a crooked line like yours...it appears perfectly parallel. I don't remember the name of the geometry principle, but you can assume that theta is 60. I used whatever geometry principle this is in my old job a fair amount, just never cared to remember the name!


edit: its not so much that you can assume theta is 60 as you can assume the angle that is not theta is 30 due to the 30 degree angle on the bottom triangle. You get to the 60 for theta by 180-90-30 = 60.