Example: In ∆ ABC, right-angled at B, AB = 24 cm, BC = 7 cm.
(i) sin A, cos A
(ii) sin C, cos C
In a given triangle ABC, right-angled at B =
Given: AB = 24 cm and BC = 7 cm
According to the Pythagoras Theorem,
Therefore, AC = 25 cm
(i) Sin A = BC/AC = 7/25
cos A = AB/AC = 24/25
(ii).Sin C = AB/AC = 24/25
Cos C = BC/AC = 7/25
Example If Sin A = 3/4, Calculate cos A and tan A.
Sin A = 3/4
Sin A = Opposite Side/Hypotenuse Side = 3/4
Now, let BC be 3k and AC will be 4k.
As per the Pythagoras theorem, we know;
Hypotenuse = Perpendicular+ Base
Substitute the value of AC and BC in the above expression to get;
Hence, AB = k
cos A = Adjacent Side/Hypotenuse side = AB/AC
cos A = k/4k = /4
Tan A = Opposite side/Adjacent side = BC/AB
Tan A = 3k/ k = 3/
Example: If A and B are acute angles such that cos A = cos B, then show that A = B.
cos A = AC/AB
cos B = BC/AB
Since, it is given,
cos A = cos B
AC/AB = BC/AB
AC = BC
We know that by isosceles triangle theorem, the angles opposite to the equal sides are equal.
Therefore, A = B