Consider the following statements:

I. The triangle is obtuse-angled triangle.

II. The sum of acute angles of the triangle is also acute.

Which of the statements given above is/are correct?

Calculation:

Given,

The sides of the triangle are:

a = 5 cm

b = 7 cm

c = 3 cm

Statement I: The triangle is obtuse-angled.

Using the Cosine Rule:

\( \cos B = \frac{a^2 + c^2 - b^2}{2ac} \)

Substitute the values for a, b = 7 and c

\( \cos B = \frac{5^2 + 3^2 - 7^2}{2 \times 5 \times 3} = \frac{25 + 9 - 49}{30} = \frac{-15}{30} = -\frac{1}{2} \)

Now, calculate angle B:

\( B = \cos^{-1}\left(-\frac{1}{2}\right) = 120^\circ \)

Thus, angle B  is \(120^\circ \), which confirms that the triangle is an obtuse-angled triangle, 

Statement II: The sum of the acute angles of the triangle is also acute.

Since the sum of the angles in a triangle is \(180^\circ \), the sum of the acute angles is:

\( A + C = 180^\circ - 120^\circ = 60^\circ \)

This confirms that the sum of the acute angles is acute,

∴ Both statements are correct.

Hence, the correct answer is Option 3.