If tan A = \(\frac{7}{24}\), find the value of sin A + cos A.

Calculations:

Given that tan A = 7/24, this means that:

Opposite (sin A) / Adjacent (cos A) = 7/24

By Pythagorous Theorem

Hypotenuse = √((Opposite side)² + (Adjacent side)²)

Hypotenuse = √((7)² + (24)²)

Hypotenuse = √(49 + 576)

Hypotenuse = √(625)

Hypotenuse = 25

So, now we have a right-angled triangle with sides 7 (opposite), 24 (adjacent), and 25 (hypotenuse).

sin A = Opposite/Hypotenuse = 7/25

cos A = Adjacent/Hypotenuse = 24/25

Then, sin A + cos A = 7/25 + 24/25 = 31/25

So, the value of sin A + cos A is 31/25.