Some Applications of Trigonometry Class 10 Maths Formulas
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Maths Formulas for Class 10 Some Applications of Trigonometry
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The height or length of an object or the distance between two distinct objects can be determined with the help of trigonometric ratios.
Line of Sight
When an observer looks from a point E (eye) at an object O then the straight line EO between the eye E and the object O is called the line of sight.
Horizontal
When an observer looks from a point E (eye) to another point Q which is horizontal to E, then the straight line, EQ between E and Q is called the horizontal line.
Angle of Elevation
When the eye is below the object, then the observer has to look up from the point E to the object O. The measure of this rotation (angle θ) from the horizontal line is called the angle of elevation.
Angle of Depression
When the eye is above the object, then the observer has to look down from the point E to the object. The horizontal line is now parallel to the ground. The measure of this rotation (angle θ) from the horizontal line is called the angle of depression.
How to convert the above figure into the right triangle.
Case I: Angle of Elevation is known
Draw OX perpendicular to EQ.
Now ∠OXE = 90°
ΔOXE is a rt. Δ, where
OE = hypotenuse
OX = opposite side (Perpendicular)
EX = adjacent side (Base)
Case II: Angle of Depression is known
(i) Draw OQ’parallel to EQ
(ii) Draw perpendicular EX on OQ’.
(iii) Now ∠QEO = ∠EOX = Interior alternate angles
ΔEXO is an rt. Δ. where
EO = hypotenuse
OX = adjacent side (base)
EX = opposite side (Perpendicular)
- Choose a trigonometric ratio in such a way that it considers the known side and the side that you wish to calculate.
- The eye is always considered at ground level unless the problem specifically gives the height of the observer.
The object is always considered as a point.
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Sin θ = \(\frac { Perpendicular }{ Hypotenuse }\)
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Cos θ = \(\frac { Base }{ Hypotenuse }\)
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Tan θ = \(\frac { Perpendicular }{ Base }\)