Given any right triangle:

Usually in any right triangle, the right angle and hypotenuse are labelled first.

The remaining sides are called the legs of the right triangle.

One of the following possibilities will then occur:

• The reference angle (θ) is chosen, and as a consequence one leg is labelled "opposite" and the other leg is labelled "adjacent".
• The legs are chosen to be labelled as "opposite" and "adjacent", and the appropriate angle is labelled as the reference angle (θ).

Recall that ratios of the lengths of corresponding sides of similar triangles are equal.

As a result, corresponding angles in similar right triangles will all have the same tangent ratio.

A person 30 m from the base of a cliff sees another person at the top of cliff at an angle of elevation of 23°? How tall is the cliff?

The angle a diagonal of a rectangle makes with the side of a rectangle is  75° . How wide is the rectangle if it is  10 m  long?

A  20 m  tall pine tree casts a shadow  12 m  long. What is tha angle of elevation of the sun?