Trig?? Right Triangle; know 3 angles and 2 sides-- need length 3rd side, Thanx?

Question

Figure is a right triangle

Angle A = 79 degrees, 56 minutes, 0 seconds
Side opposite angle A = 50 feet
Angle B = 90 degrees
Side opposite angle B = 51 feet (+/-,aprox)
Angle C = 10 degrees, 41 minutes, 0 seconds
[[ angles are from a GIS survey -- i.e. deg/minutes/seconds ]]

I believe my angle conversions to decimal would be:
angle A =79.9333, angle B = 90 angle C = 10.6833

I need to know the length of the side opposite angle C.

Then eventually the area of the triangle in sq.feet (which I'll convert to fraction of an acre, carried to 4 decimal places).

Thanks for any replies and answers!!!
TrigAnsSek

2*woops + 3*sorry!!!!

I was wrong about ANGLE A, it should be 79deg,19minutes,0sec

which as was pointed out (thanks for catching that) when added to the ANGLE C of 10deg,41minutes,0sec should equal 90.

I'll plug that correct angle in decimal version into the equation that was offered above...

Thank you all for helping.

.... good thing I'm not working for NASA!!! ;)

Answer 1

Use the Law of Sines.

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

Let's use

c/sin C = a/sin A
c = a(sin C/sin A) = 50(sin 10.6833/sin 79.9333) = 9.4319385 ft

Answer 2

Your angles do not add up correctly. But if you are sure of the lengths it does not matter. In a right triangle (90 deg) the hypotinous squared - one side squared = the square of the other side. In your case (51*51)-(50*50)=101. The square of 101 is the answer.
which is 10.04987562

Answer 3

Is something wrong with your degrees

A triangle has 180 degrees. Your degrees do not add up to 180 degrees

ie: 79deg 56 min plus 10 deg 41 min should equal 90 degrees
and they do not

Answer 4

There is something wrong in the measure of angles you have stated. The sum of angles in the problem comes to 180 degrees, 37 minutes which is absurd. Because the sum of the angles in a triangle is = 180 degrees. So please check your question first.

Answer 5

USe the following formual given Triangle ABC

SinA/a = SinB/b=SinC/c

a is the length of side a, b is the length of side b , etc
A is the angle at vertex A, Bis the angle at vertex B, etc

Answer 6

I am not a wis at trig, but
this site has a lot of answers, explainations, and find calulator
that even I could use: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/simpleTrig.html

Answer 7

I dont know