Right Triangles

The longest side is called the hypotenuse and the shorter sides the legs. In the triangle above, the legs are a and b and the hypotenuse is c.

The angles and sides of a right triangle have a connection. Sine is the ratio of the opposite leg to the hypotenuse, cosine is the ratio of the adjacent leg to the hypotenuse, and the tangent is the ratio of the opposite leg to the adjacent leg.

Example 1

The triangle below has leg lengths 3 and 4 and a hypotenuse 5

Each trigonometric function has an inverse function. They are called arcus functions - arcsin, arccosin and arctan. To determine the angle, we need these arcus functions. In calculators, they are usually denoted by the power -1.

Now, let's find angle 𝞪 of the triangle above.

We could also get the same result using cos or tan.

Example 2

find x

We know the hypotenuse but the opposite leg is unknown. We use sine

Example 3

Find x

We know the adjacent leg but the opposite leg is unknown. We use tangent

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