Helpppp!!! Me With This Trig Problem Step By Step Please

[lacticacid]

In triangle ABC side a is across from angle A, side b is across from angle B and side c is across from angle C.

If A = 14 degrees, B = 26 degrees and c = 4, find a, b and C.

Answers should be rounded to 3 decimal places.

Show at least the initial equations you set-up to find sides a and b.

[J9PUR]

Angle C is easy. The internal angles of all triangles add up to 180 degrees. Therefore if A+B+C=180, C=180-A-B. C=180-14-26. C=140 degrees.

[jim360]

Given two angles in a triangle you can always find the third through the equation A + B + C = 180. Having done so, two applications of the sine rule in the form

a/(sin A) = c/ (sin C)

to find a

b/(sin B) = c/ (sin C)

to find b

will give the remaining sides. Finally, just plug in the numbers into your calculator and make sure it is set to degree mode.

[Prudie]

If you haven't figured out from all the other trig questions you've posted that if it's a right-angled triangle you use Sin, Cos or Tan and if it's not like this one you use the Sine Rule or Cosine Rule then I don't think you should be even trying the questions as you're clearly not ready.

[Captain2]

jim360 - I think from the OPs other 'homework' questions on here, you may have left him/her way, way, way behind with your excellent answer :-))

[Jackdaw33]

Love this one.

http://funnytab.net/exam-answers/Find_X

[jim360]

Very possibly, Captain. At the moment I can't think of much else to add. At this level of mathematics it's very algorithmic really.

For a triangle, ask yourself what information do you know, and follow the "flowchart":

i) all three sides a,b,c? Cosine rule in form

Cos A = (b^2 + c^2 - a^2)/ (2 b c )

ii) any two angles A, B and one side?

iia) if the given side is a or b use sine rule straight away to find other sides:

a/(sin A) = b/(sin B) = c/ (sin C)

iib) if the given side is c (ie two angles at either end of the given side) then use sum rule for angles 180 - A - B = C and then use sine rule (as given in this question).

iii) two sides a, b and the angle between them C? cosine rule in the form

c^2 = a^2 + b^2 - (2 a b) Cos C

iiib) two sides in a right-angled triangle? Special case of above, Pythagoras Theorem

c^2 = a^2 + b^2

iv) two sides and one of the angles not between them? Sorry, you're buggered (two solutions possible).

v) all three angles? Sorry, you're buggered. (Similar triangles).