Free Study Material For RRB Examination
Subject : Mathematics (Trigonometry)
In the triangles, particularly in right angle triangles, let us
take some example from our surrounding where right triangles can be imagined to
be formed. For example:-
1. Suppose the students of a school are visiting Qutub Minar.
Now, if a student is looking at the top of the Minar, a right triangle can be
imagined to be made, as shown in figure below. Can the student find out the
height of the Minar, without actually measuring it?
2. Suppose a girl is sitting on the balcony of her house
located on the bank of a river. She is looking down at a flower pot placed on a
stair of a temple situated nearby on the other bank of the river. A right
triangle is imagined to be made in this situation as shown in Figure below. If
you know the height at which the person is sitting, can you find the width of
the river ?
3. Suppose a hot air balloon is flying in the air. A girl
happens to spot the balloon in the sky and runs to her mother to tell her
about it. Her mother rushes out of the house to look at the balloon. Now when
the girl had spotted the balloon intially it was at point A. When both the
mother and daughter came out to see it, it had already travelled to another
point B. Can you find the altitude of B from the ground?
In all the situations given above, the distances or heights
can be found by using some mathematical techniques, which come under a branch of
mathematics called ‘trigonometry’. The word ‘trigonometry’ is derived from the
Greek words ‘tri’ (meaning three), ‘gon’ (meaning sides) and ‘metron’ (meaning
measure). In fact, trigonometry is the study of relationships between the sides
and angles of a triangle. The earliest known work on trigonometry was recorded
in Egypt and Babylon. Early astronomers used it to find out the distances of the
stars and planets from the Earth. Even today, most of the technologically
advanced methods used in Engineering and Physical Sciences are based on