Suppose a straight line AX is drawn in the horizontal direction. Then the angle XAP where P is a point above AX is called the angle of elevation of P as seen from A. similarly the angle XAQ where Q is below AX, is called the angle of depression of some point Q.Line perpendicular to a plane is perpendicular to energy line lying in the plane.
To express one side of a right angled triangle in terms of the other side.
Let < ABC = θ, where ABC is a right angled triangle in which < C = 90.
The side opposite right angle C will be denoted by H (hypotenuse), the side opposite to angle 4:07 PM will be denoted by o (opposite) and the side containing the angle θ (Other than H) will be denoted by A i.e., adjacent side.Then from the figure it is clear that
O = A (tan θ) or A = O (cot θ)
I.e., opposite = Adj tan θ
Also O = H (sin θ or A = H (cos θ
Or opposite = Hyp sin θ
Or Adj = Hyp (cos θ)
Geometrical properties for a triangle: In a triangle the internal bisector of an angle divides the opposite side in the ratio of the arms of the angle.BD/DC = c/b
In an isosceles triangle the median is perpendicular to the base.
In similar triangles the corresponding sides are proportional.
The exterior angle is equal to sum of interior opposite angles.
θ = A + B
Example: A ladder rests against a wall at an angle X to the horizontal its foot is pulled away from the wall through a distance a so that it slides a distance b down the wall making an angle β with the horizontal, show that a = b tan [(α + β)/2]
Solution: b = BC = AB – AC = lsin α – lsin βa = PQ = AQ – AP = lcos β – lcos α
a/b = cosα – cosβ / sinβ – sinα = tan [(α + β)/2]