How do I solve this? (PreCalculus stuff)?

Question

Ok, here are the triangle's details... (the triangle looks kind of like an acute triangle, I can't really draw it on here though)

-there is right angle on the lower right
-there is a 61 degree angle on the lower left
-the very top angle on the triangle is unknown, this also needs to be solved (i think)
-the bottom side (b) equals 10 cm
-the unfinished side (a) is the side that need to be solved for
-side "c" (hypotenuse) is not needed in this problem

Please help! Everybody forgot everything over the Christmas Break.

Answer 1

start by finding the angle of the top angle.
180-90-61= 29 degrees

then remember: soh, cah, toa
tan29=10cm/x
x=18.0
sin29=10cm/c
c=20.62

Answer 2

If you're sure that it's a right triangle, then life is easy. First off, you know that the sum of the angles in a triangle is 180 degrees. That being the case, then the upper angle (which, by the way, you don't need to know) is 180 - 90 - 61 = 29 degrees.

Now: you have a right triangle, an acute angle of 61 degrees, the length of the adjacent leg, and you're looking for the length of the opposite leg. You need a trig function that relates the opposite to the adjacent. You'll find it in the tangent. So:

tan 61 = a/10

and you can solve for a from there.

Answer 3

Use Trigonometry. Easy!

Tan = opp/adj
Tan61degrees = a/10
10 x tan 61 = a