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

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° =

tan60° =

By comparing the equations,

Then, BC > AC

Hence, The required correct statement in △ABC are BC > AC and BC < AB.

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x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.