Hypotenuse, Adjacent and Opposite Sides.
In the following right triangle PQR,
Note: The adjacent and the opposite sides depend on the angle θ. For complementary angle of θ, the labels of the 2 sides are reversed.
Identify the hypotenuse, adjacent side and opposite side in the following triangle:
a) for angle x
b) for angle y
a) For angle x: AB is the hypotenuse, AC is the adjacent side , and BC is the opposite side.
b) For angle y: AB is the hypotenuse, BC is the adjacent side , and AC is the opposite side.
The following diagram show how to use SOHCAHTOA for a right triangle.
How to identify the Opposite Sides, Adjacent Sides and Hypotenuse of a Right Triangle?
Definition of Cos, Sin, Tan, Csc, Sec, Cot for the right triangle
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
csc x = 1/sin x = hypotenuse/opposite
sec x = 1/cos x = hypotenuse/adjacent
cot x = 1/tan x = adjacent/opposite
Using the Sine Formula (the SOH formula)
The first part of this video will explain the difference between the hypotenuse, adjacent and opposite sides of a right triangle. Then it shows how to use the sine formula (the SOH formula).
Sine = Opposite over the Hypotenuse
Using the Cosine Formula (the CAH formula)
Cosine = Adjacent over Hypotenuse
Using the Tangent Formula (the TOA formula)
Tangent = Opposite over Adjacent
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.