The document explains how to use the soh cah toa trigonometric relationships to solve for the opposite (o) and adjacent (a) sides of a right triangle given an angle of 30° and a hypotenuse of 40”. It details the calculations step-by-step, resulting in an opposite side of 20” and an adjacent side of approximately 34.64”. Minor differences in results are attributed to rounding and the importance of using precise values in calculations is emphasized.

1. 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

2. Continue to solve by using basic Algebra:
Angle = 30°
Hypotenuse is 40”
S = O/H
40”
Sin(30) = O/40
O=20”
.5 = O/40
Multiply both sides by 40 to solve for O:
(.5) x 40 = (O/40) x 40 30°
20 = O
So the length of the opposite side is 20”

3. 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.