There are two triangles that touches each other...

[maemae]

Hi, I am completely stumped on this geometry question and I will try my best to word it:

There are two triangles that touches each other where triangle ABO shares its AO side with triangle AOC to make one large triangle ABC. Triangle ABC, where A is 75 degrees, B is 60 degrees and C is 45 degrees. AO is perpendicular to line BC.

Length of AB is 1, length of AC and BC are not given. What is the length of BC?

Thank you very much!

 

[Denis]

Did you realise that triangles AOB and AOC are right triangles?
Do you "see" that angleCAO = 45 degrees and angleBAO = 30 degrees?

You ok now?

 

[Mrspi]

Hi, I am completely stumped on this geometry question and I will try my best to word it:

There are two triangles that touches each other where triangle ABO shares its AO side with triangle AOC to make one large triangle ABC. Triangle ABC, where A is 75 degrees, B is 60 degrees and C is 45 degrees. AO is perpendicular to line BC.

Length of AB is 1, length of AC and BC are not given. What is the length of BC?

Thank you very much!

Nice job on the description! I was able to draw the diagram with no difficulty.

Triangle ABO is a 30-60-90 triangle; its hypotenuse AB = 1. AO is the LONG LEG of this triangle, and OB is the short leg. You should be able to find both AO and OB using the 30-60-90 theorem.

Note that triangle AOC is a 45-45-90 triangle, so legs AO and OC are the same length. You'll have found AO in the previous step, so you know OC also.

And,

CO + OB = BC