How can I find angle A in a right triangle without using a calculator?

[wrekoniz3]

Homework Statement

a right triangle. hypotenuse is 10, the opposite is 8, and the adjacent is 6

Sine .6

Cosine .8

Tangent .75

i need to find angle A (aka Alpha in the problem) With out using a graphing or scientific calculator.

Homework Equations

i was told to use Gregory;s formula:

http://crazyimage.net/images/untitled.png

the numbers for the problem are plugged in. I am really lost with the whole thing. lol

The Attempt at a Solution

On the ti-83 i do the inverse sine button .6 and i get the answer which is 36.9 degrees.

if the calculator can do it that easy there has to be an easier way to do this...


thanks in advance!

i have a test on this on wednesday :(

-Dom

 

[HallsofIvy]

No, the fact that a calculator can do it does NOT prove that there is an "easier" way. A calculator does a lot of tedious computations very quickly. Strictly speaking a calculator does use a faster algorithm than you are given but you would still find it very tedious and slow.

You could, of course, put your calculator in radian mode before you take the inverse tangent if you want to check you calculation (which is pretty accurate).