Just imagine how humans could measure the height of Mount Everest![br]It would be practically impossible for a person to hold a measuring tape and climb the mountain to measure the height.[br]Then how did they do it?[br]Trigonometry comes to our rescue.[br]How is that? Let's see.[br][br]Imagine a person seeing the top of Mount Everest from its foot at some angle [math]\alpha[/math]. And the distance between the person and the perpendicular to the ground from the peak is also measurable.[br]You might be getting the idea now![br][br]If we draw a right-angle triangle with the same angle [math]\alpha[/math] and measure the value of tan[math]\alpha[/math].[br][br]Since [math]tan\alpha=\frac{Opposite}{Adjacent}[/math] and we know the value of adjacent that is the distance between the person and the perpendicular to the ground from the peak we can multiply [math]tan\alpha[/math] and the adjacent distance to get the opposite side value that is nothing but the height of the mounatin

Here CD is the height of the mountain.[br]Angle [math]\alpha[/math] is made by you when you look at the mounatin.[br]AD is the distance between your foot and the perpendicular from the peak of the mountain.

This is how we can use trigonometry to calculate heights and distances.