In any triangle, two of the interior angles are always acute (less than 90 degrees)^*, so there are three possibilities for the third angle:

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• Less than 90° - all three angles are acute and so the triangle is acute.
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• Exactly 90° - it is a right triangle
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• Greater than 90° (obtuse): the triangle is an obtuse triangle
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The oblique triangle means a triangle that contains no right angle.

Therefore that triangle is either acute triangle or obtuse triangle.

The formula for the area of oblique triangle is Area = 1/2 bc sin A = 1/2 ab sin C = 1/2 ac sin B.

if angle A is 90^o, the formula gives the area for a right triangle :

Area = 1/2 bc sin A = 1/2 bc sin 90^o = 1/2 bc = 1/2 (base)(height).

The base of the triangle is 8 units and height is 3 units and its area is 12 square units.

To check  the above triangle is right angle triangle, as follows :

Area = 1/2 (base)(height).

12 = 1/2 (8)(3)

12 = 24/2

12 = 12.

The above statement is true, so the given triangle is right angle triangle.

To tell  the above triangle is right angle triangle, by use another method as follows :

Let the sides of the triangle are a = 8 units, b = 3 units and c.

Here to find the remaining side by use the Pythagorean Theorem, (hypotenuse)² = (opposite)² + (adjacent)²

c = √[ (3)² + (8)² ] = √[ 9 + 64 ] = √(73).

a = 8, b = 3 and c = √(73) ≅ 8.544.

a² = 64, b² = 9 and c² = 73.

The formula for the area of oblique triangle is Area = 1/2 bc sin A = 1/2 ab sin C = 1/2 ac sin B

Find angle A:

Area = 1/2 bc sin A

12 = (1/2) (3)(8.544) sin A

24 = (3)(8.544)sin A

8/(8.544) = sin A

0.936 = sin A

A ≅ 69.444

Find angle B:

Area = 1/2 ac sin B

12 = (1/2) (8)(8.544) sin B

3 = (8.544)sin B

3/(8.544) = sin B

0.351 = sin B

B ≅ 20.556.

The remaining angle is C = 180^o - (69.444^o + 20.556^o) = 180^o - 90^o = 90^o.

The given triangle is right angle triangle.