Question

Explain the fact that the values of the trigonometric ratios remain same irrespective of the length of the side of different right angled triangle

Answer 1

Answer:

BC = a = 1 cm,

AC = b = 1 cm,

AB = c = √2 cm.

Angle A = 45°.

So, Tan A = Opposite / Adjacent = 1/1 = 1cm

Also, Tan(45°) = 1

Now, Lets say, I’ve extended and increased the size of BC to 2 cm.

If I increase BC to 2 cm without increasing AC and draw a line from A to B, then angle A increases.

So, to maintain A as 45°, we need to increase AC and BC simultaneously.

So, as BC increases, AC also increases and BC/AC = 1 always..

i.e., Tan 45° = opposite / adjacent = BC / AC = 1 always