Use sine, cosine, or tangent to recover right-triangle side lengths. A checkable formula accompanies right-triangle sides instead of leaving an unexplained number.
With hypotenuse 10 and angle 30°, the opposite side is 5 and the adjacent side is about 8.6603.
SOHCAHTOA encodes sin=opposite/hypotenuse, cos=adjacent/hypotenuse, and tan=opposite/adjacent.
Circle the known side and target side, select the ratio containing both, and solve the proportion. SOHCAHTOA also connects to tangent application.
It turns one acute angle and one side into the missing right-triangle sides.
The words opposite and adjacent depend on the chosen acute angle, not on how the drawing sits on the page. If the SOHCAHTOA assumptions do not fit, consider complete triangle.
Start the SOHCAHTOA review with Known side and requested relationship. Compare Known side and requested relationship with its source, then test Acute angle in degrees in a second SOHCAHTOA run without changing the first SOHCAHTOA case.
SOHCAHTOA uses Known side and requested relationship, Acute angle in degrees, and Known side length. Sketch the quadrant, triangle, or wave position before calculating. The expected sign and rough magnitude provide a stronger check than repeating the same keystrokes.
For this sohcahtoa result, retain the measured lengths at source precision and round only the requested geometric result.
Rework SOHCAHTOA without copying Right-triangle sides. Begin with Known side and requested relationship and preserve Acute angle in degrees. Predict the scale of the SOHCAHTOA answer, then compare it with Right-triangle sides. Store a changed Known side length as another SOHCAHTOA case.
Challenge Right-triangle sides with a nearby value of Known side and requested relationship. Leave Acute angle in degrees fixed during the SOHCAHTOA trial. The direction of the new Right-triangle sides should agree with the underlying SOHCAHTOA relationship.
SOHCAHTOA encodes sin=opposite/hypotenuse, cos=adjacent/hypotenuse, and tan=opposite/adjacent.
It turns one acute angle and one side into the missing right-triangle sides.
The words opposite and adjacent depend on the chosen acute angle, not on how the drawing sits on the page.
Circle the known side and target side, select the ratio containing both, and solve the proportion.