Q)  If in a triangle ABC right angled at B, AB = 6 units and BC = 8 units, then find the value of sin A cos C + cos A sin C.

Ans: 

Step 1: Let’s make a diagram to better understand the question:

Here Δ ABC is a right angle triangle and ∠B is 90.

we are given AB = 6 units, BC = 8 units

Step 2: By Pythagoras theorem, let’s calculate the value of side AC:

AC² = AB² + BC²

∴ AC² = (6)² + (8)²  = 36 + 64

= 100 = (10)²

∴ AC = 10 units

Step 3: From the diagram, let’s calculate the different values:

sin A =

and cos A =

Similarly, sin C =

and cos C =

Step 4: Let’s put the values now:

sin A cos C + cos A sin C

=

=

=  = 1

Therefore, the value of sin A cos C + cos A sin C is 1.

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