Answered

On a piece of paper, use a protractor to construct △ABC with m∠A=30° , m∠B=60° , and m∠C=90° .


Which statements about the triangles are true?


Select each correct answer.

A. BC>AB

B. BC>AC

C. BC<AC

D. BC<AB

Verified Answer :

wolf1728

Statements C and D are true

View image wolf1728

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° = \(\frac{AC}{BC}\)

tan60° = \(\frac{\sqrt{3} }{1}\)

By comparing the equations,

\(\frac{AC}{BC} = \frac{\sqrt{3} }{1}\)

\(AC = \sqrt{3} BC\)

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