The required correct statement in △ABC are BC > AC and BC < AB.
Given that,
To construct △ABC with m∠A=30°, m∠B=60°, and m∠C=90°.
We have to find,
The statements about the triangles are true.
According to the question,
In △ABC
This means that the side opposite to the right angle in the triangle is AB.
Since, the side opposite to the right angle is the hypotenuse and is the longest side of the triangle, thus AB cannot be shorter than any other side of the triangle.
Then, BC < AB.
And, In the triangle △ABC ,
tan60° = [tex]\frac{AC}{BC}[/tex]
tan60° = [tex]\frac{\sqrt{3} }{1}[/tex]
By comparing the equations,
[tex]\frac{AC}{BC} = \frac{\sqrt{3} }{1}[/tex]
[tex]AC = \sqrt{3} BC[/tex]
Then, BC > AC
Hence, The required correct statement in △ABC are BC > AC and BC < AB.
For the more information about Trigonometry click the link given below.
https://brainly.com/question/14034633
