Using SOH CAH TOA To solve for O: Look at what is known and what is being solved for to determine which formula to use. Angle (Θ) = 30° H= 40” H = 40” O=? SOH CAH TOA:O? SOH can be used- S = O/H Sin(30)= O/40 Θ=30° Plug the formula into a scientific calculator: A? Sin 3 0 = 0.5
Continue to solve by using basic Algebra:Angle = 30°Hypotenuse is 40”S = O/H 40”Sin(30) = O/40 O=20”.5 = O/40Multiply both sides by 40 to solve for O:(.5) x 40 = (O/40) x 40 30°20 = OSo the length of the opposite side is 20”
Now solve for Adjacent: SOH CAH TOA In this case, cosine or tangent could be used. CAH: Cos(30) = A/H Cos(30) = A/40 (.866) = A/40 (.866) x 40 = (A/40) x 40 34.64=A H = 40” Adjacent side is equal to 34.64”O = 20” TOA: Tan(30) = O/A (.577) = 20/A (.577) x A=( 20/A) x A 30° (.577 x A) = (20) (.577 x A) /.577 = (20) /.577 A=? A = 34.66 Adjacent side is equal to 34.66” The slight difference is due to rounding up or down , and van be avoided by following through on the calculator with given answers rather than rounding up or down.