Tan Formula
Out of the three main primary functions in trigonometry is tan. The ratio of the length of the opposite side to that of the adjacent side in any rightangled triangle is said to be the tan function. Depending upon the quadrants, the tan function can have both positive as well as negative values. The Tan formula is used to find the value of the angle if the opposite side and the base are known to us. The tan formula is explained below along with solved examples.
What Is the Tan Formula?
Tan formula is the ratio of the length of the opposite side to the angle and adjacent side to the angle. The tan formula can also be used to find the lengths of the side of the triangle if we know the angle and either side. Tan Formula can be expressed as,
tanθ = Opposite Side/Adjacent Side
or
tanθ = O/A
Where,

O = Opposite Side

A = Adjacent Side

Example 1: Calculate the tangent angle of a rightangle triangle, by using the tan formula, whose opposite and adjacent sides are 12 cm and 14 cm respectively.
Solution
To find: tanθ
Given:
A = 12cm
Opposite Side = 14cm
Using the Tan Formula,
tanθ = O/A
tanθ = 12/14
tanθ = 0.85Answer: Tanθ is 0.85.

Example 2: Find the angle of a right triangle, by using the tan formula, whose adjacent and opposite are equal to each other.
Solution
To find: Angle
Given: Opposite Side = Adjacent SideUsing the Tan Formula,
tanθ = O/A
Put the values,
tanθ = O/A
tanθ = A/A
tanθ = 1
θ = 45
Answer: Angle is 45 degrees.
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