# Formulas For Height And Distance

## Height and Distances related Formulas

Trigonometry was invented because its need arose in astronomy. Since then the astronomers have used it, for instance, to calculate distances from the Earth to the planets and stars. Trigonometry is also used in geography and in navigation. To get to know this application of Trigonometry better we have this page of Formulas For Height And Distances. The knowledge of trigonometry is used to construct maps, determine
the position of an island in relation to the longitudes and latitudes.

In this page we are going to learn about various Formulas for Height and Distances which will include different types of trigonometric ratios and figures. For your knowledge

Height : The measurement of an object vertically known as Height.

Distance is the measurement of an object from a particular point in the horizontal direction.

### Height and Distance Formulas

• There are basically two terms associated with heights and distances which are as follows :
• Angle of Elevation.
• Angle of Depression.

### Formulas for Angle of Elevation

• The Angle of elevation of the point viewed is the angle formed by the line of sight with the horizontal when the point being viewed is above the horizontal level, i.e., the case when we raise our head to look at the object

### Formulas for Angle of Depression

• The angle of depression of a point on the object being viewed is the angle formed by the line of sight with the horizontal when the point is below the horizontal level, i.e., the case when we lower our head to look at the point being viewed. ### Height and Distance Formulas for Trigonometric ratio

• ΔABC is a right angled triangle where is AB is the perpendicular, AC is the hypotenuse, and BC is the base.

Then,

• Sin θ  = $\frac{AB}{AC}$
• Cos θ = $\frac{BC}{AC}$
• Tan θ  = $\frac{AB}{BC}$
• Cosec θ  = $\frac{AC}{AB}$
• Sec θ  = $\frac{AC}{BC}$
• Cot θ  = $\frac{BC}{AB}$
• Trigonometrical Identities:
• sin2θ + cos2 θ = 1
• 1 + tan2θ = sec2 θ
• 1 + cot2θ = cosec2 θ ### Definition of Harmonic Progression (H.P)

Harmonic progression is the series when the reciprocal of the terms are in AP.

For example, $\frac{1}{a}, \frac{1}{ (a + d)}, \frac{1}{(a + 2d)}$…… are termed as a harmonic progression as a, a + d, a + 2d are in Arithmetic progression.

• First term of a HP is $\frac{1}{a}$
• There are many Application of Harmonic Progressions.

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