What is the value of tan 30°?

What is the value of tan 30°?

• A. 0
• B. 0.5
• C. 0.577
• D. 1

Answer: (C)

The value of tan 30° is derived from the properties of a 30-60-90 triangle. In such a triangle, the lengths of the sides are in the ratio of 1:√3:2. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. For an angle of 30° in a 30-60-90 triangle, the side opposite the angle (which is 30°) has a length of 1, while the adjacent side (which corresponds to the 60° angle) has a length of √3. Therefore, we calculate: tan 30° = (opposite side) / (adjacent side) = 1 / √3. To express this in a more usable form, we can simplify it further by multiplying the numerator and denominator by √3, yielding: tan 30° = √3 / 3. If you evaluate √3 (approximately 1.732), dividing this by 3 results in approximately 0.577, which corresponds to the value of tan 30°. Hence, the correct value is approximately 0.577, confirming that tan 30° equals 0.

The value of tan 30° is derived from the properties of a 30-60-90 triangle. In such a triangle, the lengths of the sides are in the ratio of 1:√3:2. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side.

For an angle of 30° in a 30-60-90 triangle, the side opposite the angle (which is 30°) has a length of 1, while the adjacent side (which corresponds to the 60° angle) has a length of √3. Therefore, we calculate:

tan 30° = (opposite side) / (adjacent side) = 1 / √3.

To express this in a more usable form, we can simplify it further by multiplying the numerator and denominator by √3, yielding:

tan 30° = √3 / 3.

If you evaluate √3 (approximately 1.732), dividing this by 3 results in approximately 0.577, which corresponds to the value of tan 30°.

Hence, the correct value is approximately 0.577, confirming that tan 30° equals 0.