Question

Use a special right triangle to express tan 30 degrees as a fraction and as a decimal to the nearest hundredth. Select all that apply.

a) (1/√3), 0.58
b) (√3/3), 0.87
c) (√3/2), 0.86
d) (1/2), 0.50

Answer 1

The tangent of 30 degrees can be expressed as a fraction by using a special right triangle, resulting in 1/√3 or √3/3 after rationalization. It is approximately 0.58. Therefore, the correct answers are (a) and (b).

Step-by-step explanation:

To express tan 30 degrees as a fraction and as a decimal, we can use one of the special right triangles, specifically the 30-60-90 triangle. In this triangle, the sides have the ratio 1:√3:2. Since the tangent function is the ratio of the opposite side over the adjacent side.

Tan 30 degrees is the length of the side opposite the 30-degree angle (1) divided by the length of the side adjacent to the 30-degree angle (√3). Therefore, tan 30 degrees can be expressed as 1/√3. By rationalizing the denominator, we get √3/3.

As a decimal, tan 30 degrees is approximately 0.58 to the nearest hundredth. Therefore, the correct answers are option (a) (1/√3), 0.58 and option (b) (√3/3), 0.58. Options (c) and (d) do not correctly represent the tangent of 30 degrees.