For AI agents: use /llms.txt for the Nakafa content index.
In a right triangle, the tangent of angle is the ratio between the length of the opposite side and the adjacent side. This is very different from sine, which compares the opposite side to the hypotenuse, or cosine, which compares the adjacent side to the hypotenuse.
For example, if we have a right triangle with angle , then:
The value of tangent changes according to the angle. For example, .
The tangent trigonometric ratio is very useful for solving various real-life problems, especially when we want to calculate:
Imagine we want to measure the height of a tree, building, or other tall object. We can use the tangent ratio with the following steps:
There are two ways we can use to solve problems using tangent:
We can use the principle of similar triangles to solve problems. If we have two triangles with the same shape (similar), then the ratio of their sides will be the same.
For example, if we have shadows from three objects of different heights (child, teenager, and adult), we can create the equation:
With this equation, if we know the child's height (e.g., ), their shadow length (), and the teenager's height (), we can calculate the teenager's shadow length:
Another more direct way is to use the tangent trigonometric ratio. We know that:
For example, if we have a sun elevation angle of () and want to calculate the shadow length of a teenager with height :
