General Mathematics Study Notes
Trigonometric Ratios and Right Triangles
Trigonometric ratios are relationships between the sides of a right triangle. They apply only to
triangles containing a right angle ().
โข Sine (sin): Ratio of the opposite side to the hypotenuse. Formula: $$\sin \theta =
\frac{\text{opposite}}{\text{hypotenuse}}$$
โข Cosine (cos): Ratio of the adjacent side to the hypotenuse. Formula: $$\cos \theta =
\frac{\text{adjacent}}{\text{hypotenuse}}$$
โข Tangent (tan): Ratio of the opposite side to the adjacent side. Formula: $$\tan \theta =
\frac{\text{opposite}}{\text{adjacent}}$$
Example: If opposite = 3 and hypotenuse = 5, then .
Angles of Elevation and Depression
โข Angle of Elevation โ Measured upward from the horizontal line. Used when the object
being observed is above the observer.
โข Angle of Depression โ Measured downward from the horizontal line. Used when the
object is below the observer.
Both angles are applied in height and distance problems, such as finding the height of a
building or the depth of a valley.
Oblique Triangles and Area Formulas
An oblique triangle is a triangle that does not contain a right angle. Two key area formulas exist
for such triangles.
Area Using Two Sides and the Included Angle
where and are two sides and is the angle between them.
Heronโs Formula (Area Using Three Sides)
where , , are the side lengths and is the semi-perimeter. This formula works for any triangle,
including oblique.
