math help...someone who is good at triangles?

Question

problem one:

angle A is 60 angle B is 30 and angle C is 90

side CB is 12 what is side AB?

problem two:

its the same angles as problem one

but side AB is 4 radical 3 what are the other two sides?

Answer 1

Both triangles have a 30-60-90 degree angle scheme...they are both 30-60-90 triangles. These triangles have a few special properties, namely when it comes to the length of sides. If the length of the side opposite the 30 degree angle is x, then the hypotenuse is 2x and the remaining side is x*sqrt(3).

Therefore, for your first question, if CB is 12, then we need to divide by sqrt(3) and then multiply by 2 to get AB, or the hypotenuse. Your final answer would be 24/sqrt(3) or 8*sqrt(3), depending if your teacher hates radicals in the denominator.
For your second question, AB is the hypotenuse, so the side opposite the 30 degree angle, AC, is 1/2 the length of AB, or 2 sqrt(3). Then, for the last side, BC, it's 2sqrt(3) times sqrt(3), or 2*3=6.

Note that I've replaced the radical with sqrt, which means square root. Hope that helps.

Answer 2

You have not indicated,how you want it to be solved...with the help of Geometry or Trigonmetry.Anyhow,I am solving it in both ways>It is upto you to choose the process.You have already got a triangle ABC whose angles A,B andC are60,30 and 90 degrees respectively.From angle C,an angle BCD is drawn equal to 60degrees,which intersects AB at point D. Now,in triangle BCD,angles BCD and DBC are 60.Therefore,BDC is 180-(60+60)=60 .Therefore,BDC is an equilateral triangleDSo BD=CD=BC=12 now,in triangleACD angle A is 30 (given) and angle ACD is 90-60=30. Therefore ACD is an isoceles triangle Therefore,AD=CD=12 Therefore,AB=AD+BD=12+12=24 From the above proof,you can find out that if length of AB is given,the lengths of AC and BC will be half of AB .If you want trigonmetrical calculations.please ask the question again or ask the authorities of yahoo Answers to send an e-mail directly to me so that I can send a rply with figures drawn.Sorry,I am an old man and am playing with computer for the last 6 months only and cannot draw a figure with its help.however,i have a scanner and can help you by sending a drawn figure

Answer 3

AB is 6 because it's 30-60-90 triangle theorem. Is CB the hypothenus? If not then AB is 12*square root of 3

Answer 4

The answer to your first question is 13.

The answer to your second answer involves looking up the sine/cosine/tangent table. So, the equation for solving the value of the hypotenuse is going to be:

the value of sin 30 degrees = 4 radical 3 divided by the value of the hypotenuse.

Solve for the value of the hypotenuse.

After you get the value of the hypotenuse, then just plug in the numbers to the pythagorean's theorem, which is:

a squared + b squared = c squared

solve for b and you'll get the answer(s) to your second question.

Answer 5

please dont remind me of school i just graduted