Question

solve for r

There is a right triangle with the hypotenuse as r , the angle as 45 degrees and opposite side as 20.

I am having a hard time finding this out. I had tan 45 = 1.61 20(1.61) = 32.4 but this is wrong.

Answer 1

A basic rule for right triangles is sine(theta) = opposite/hypotenuse

20 = your opposite side
theta is your angle

rearrange to fit your problem:
hypotenuse = opposite/sin(theta)
plug in and solve
make sure your calculator is in degrees, not radians too.

Answer 2

what you did wrong was this:

tan(theta) = opposite / adjacent

An easy trick to remember is SOHCAHTOA (pronounced so-ka-toe-a):

sin (S) is opposite(O)/hypotenuse(H)
cos (C) is adjacent (A)/hypotenuse(H)
tan (T) is opposite (O)/adjacent (A)

I'm in college calculus now, and I still use that trick to remember.