Final answer:
Without additional information regarding the angle or the other sides of the triangle, the specific values of sin, cos, and tan cannot be determined solely with one side length of 12. To calculate these, knowledge of at least one non-right angle or another side length is necessary.
Step-by-step explanation:
To calculate the sin, cos, and tan of an angle in a right-angled triangle when given one side, we need to know at least one other side or angle to use trigonometric ratios. The 'one side = 12' does not provide enough information to determine these values directly unless it is the hypotenuse and we know the angles, or if it is a leg and we know one angle besides the right angle. Trigonometrical relationships (sin, cos, tan) are defined as the ratios of the sides of right-angled triangles:
- sin = opposite/hypotenuse
- cos = adjacent/hypotenuse
- tan = opposite/adjacent
Without additional information about the angle or the lengths of the other sides, the specific values of sin, cos, and tan cannot be determined.
However, some common identities can be used if the angle is known, such as:
- The Law of Sines which relates the lengths of the sides of any triangle to the sines of its angles
- The Law of Cosines for calculating a side of a triangle when the other two sides and the included angle are known
- Trigonometric identities like sin(2α) = 2sinαcosα and cos(2α) = cos²α - sin²α which relate the trigonometric ratios of multiple angles.