Application of Trigonometry in Daily Life



Exterior Angles

Exteriors angles are angle between any side of the shape and a line extended from the next side or outwards. 
When the two parallel lines are cut by a transversal, then the angles which are formed in the outside of the lines are called as exterior angles.  
If you are adding the interior and exterior angles of any shape on the same vertex, you will get a straight line of about 180˚.
 
With reference to the above figure the exterior angle LACD is as the side of BC of ∆ ABC is extended to the next side D. 
The exterior angles LACD are supplemental to the adjoining interior angles LABC. 
The addition of interior and exterior angles are equal to 180˚.
LACD + LACB = 180˚

Exterior Angles of Triangles

The exterior angle of triangles is angle in between one side of the triangle and the extension of an adjacent side. 
Exterior angles of triangles are formed when one side of the triangle is extended to the adjacent side of the triangle. 
An exterior of triangle is equal to the sum of the addition of the opposite two interior angles.

Ld = La + Lb

Finding Exterior Angles

Finding the exterior angles with reference to below given figure.
We know that sum of the adjacent angles inside the triangles are forming a straight line.
So, 
x + 58˚ = 180˚
x = 180˚-58˚
x = 122˚
We also know that sum of angles of inside the triangles are equal to 180˚.
So,
x + y + z = 180˚
60˚ + y + 58˚ = 180˚
y = 62˚
We know that the exterior angle of triangle is equal to the sum of the opposite interior angles.
So,
50˚ + x = 92˚
x = 92˚ - 50˚ = 42˚
We also know that that the sums of the interior angles and adjacent exterior angles are equal to 180˚.
So,
y + 92˚ = 180
y = 180˚ - 92˚ = 88˚

Exterior Angles Definition

Exterior angles are defined as it is the angle between the side of a shape and an extended adjacent side.

Exterior Angles of a Triangle
The exterior angles of a triangle measure are equal to sum of its two remote angles. 
In other wards an exterior angles of a triangle is equal to the sum of the two opposite sides of the interior angles.
We know that the sum of the angles inside the triangles is equal to 180˚.
X + Y + Z = 180˚ --------------> (1)
We also know that the sum of the measure of angle w and angle z is equal to 180˚.
W + Z = 180˚ ---------------> (2)
From the equation 1 and 2
Z = 180˚ – X – Y
W + 180˚ – X – Y = 180˚
W = X + Y
So the measure of exterior angles of triangle is equal to the sum of the measures of the two remote interior angles of the triangle.