Introduction Of Trigonometry

We have seen triangles and their properties in previous classes. There, we observed different daily life situations where we were using triangles.

Let’s again look at some of the daily life examples.

Electric poles are present everywhere. They are usually erected by using a metal wire. The pole, wire and the ground form a triangle. But, if the length of the wire decreases, what will be the shape of the triangle and what will be the angle of the wire with the ground ?

A person is whitewashing a wall with the help of a ladder which is kept as shown in the adjacent figure on left. If the person wants to paint at a higher position, what will the person do? What will be the change in angle of the ladder with the ground ?

In the temple at Jainath in Adilabad district, which was built in 13th century, the first rays of the Sun fall at the feet of the Idol of Suryanarayana Swami in the month of December. There is a relation
between distance of Idol from the door, height of the hole on the door from which Sun rays are entering and angle of sun rays in that month. Is there any triangle forming in this context?

In a play ground, children like to slide on slider and slider is on a defined angle from earth. What will happen to the slider if we change the angle? Will children still be able to play on it?

The above examples are geometrically showing the application part of triangles in our daily life and we can measure the heights, distances and slopes by using the properties of triangles. These types of problems are part of ‘trigonometry’ which is a branch of mathematics.

Now look at the example of a person who is white washing the wall with the help of a ladder as shown in the previous figure. Let us observe the following conditions.

We denote the foot of the ladder by A and top of it by C and the point of joining height of the wall and base of the ladder as B. Therefore, ΔABC is a right angle triangle with right angle at B. The angle between ladder and base is said to be θ.
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