Formulae
1. Trigonometry:
In a right angled △ABC, where ∠ACB = θ,
i. sin θ = Perpendicular/Hypotenuse = AB/BC ;
ii. cos θ = Base/Hypotenuse = CA/CB ;
iii. tan θ = Perpendicular/Base = AB/CA ;
iv. cosec θ = 1/sin θ = CB/AB ;
v. sec θ = 1/cos θ = CB/CA ;
vi. cot θ = 1/tan θ = CA/AB ;
2. Trigonometrical Identities:
i. sin2 θ + cos2 θ = 1
ii. 1 + tan2 θ = sec2 θ
iii. 1 + cot2 θ = cosec2 θ
3. Table 1: Trigonometric Ratios of Standard Angles
Angle of Elevation:| ∠θ | 0° | (π/6) 30° | (π/4) 45° | (π/3) 60° | (π/2) 90° |
| sin θ | 0 | ½ | 1/√2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | 1/√2 | ½ | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | Not Defined |
| cosec θ | Not Defined | 2 | √2 | 2/√3 | 1 |
| sec θ | 1 | 2/√3 | √2 | 2 | Not Defined |
| cot θ | Not Defined | √3 | 1 | 1/√3 | 0 |
Suppose a man from a point C looks up at an object A, placed above the level of his eye. Then, the angle which the line of sight makes with the horizontal through C, is called the angle of elevation of A as seen from C.
∴ Angle of elevation of A from C = ∠ACB.
Angle of Depression:
Suppose a man from a point C looks down at an object A, placed below the level of his eye, then the angle which the line of sight makes with the horizontal through C, is called the angle of depression of A as seen from C.
Exercise : Height and Distance MCQ Questions and Answers
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