Height and Distance

introduction to Height and Distance

trignomentry :

In a right-angled\( \triangle\) OAB, where \(\angle \mathrm{BOA}\)=\(\mathrm{\theta}\)

triangle

  • \(\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }}=\frac{A B}{O B}\)
  • \(\cos \theta=\frac{\text { Base }}{\text { Hypotenuse }}=\frac{O A}{O B};\)
  • \(\tan \theta=\frac{\text { Perpendicular }}{\text { Base }}=\frac{A B}{O A};\)
  • \(\csc \theta=\frac{1}{\sin \theta}=\frac{O B}{A B}\);
  • \(\sec \theta=\frac{1}{\cos \theta}=\frac{O B}{O A}\)

Trigonometrical Identities:

  1. \(\sin ^{2} \theta+\cos ^{2} \theta=1\)
  2. \(1+\tan ^{2} \theta=\sec ^{2} \theta\)
  3. \(1+\cot ^{2} \theta=\csc ^{2} \theta\)

Value of T ratios

Value of T rotations

t ratios

Angle of Elevation:

hl

Suppose a man from a point O looks up at an object P, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through O is called the angle of elevation of P as seen from O.

\(\therefore\)The angle of elevation of P from O= \(\angle \mathrm{AOP}\)

An angle of Depression:

sl2

 

   Suppose a man from a point O looks down at an object P, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through O is called the angle of depression of P as seen from O.