Which equation can be used to solve for b?

To determine the appropriate equation to solve for b, let’s analyze the options provided:

• 8tan(30°)
• 8sin(30°)

In trigonometry, tan and sin are functions that relate the angles of a triangle to the ratios of its sides. The angle of 30 degrees has known values for sine and tangent:

• tan(30°) = 1/√3 ≈ 0.577
• sin(30°) = 1/2 = 0.5

To decide which equation is suitable, we need context about what b represents. If b is the length of a side in a triangle and we’re using a right triangle where an angle measures 30 degrees, the sine function would typically relate the opposite side to the hypotenuse. Therefore, we can express b in terms of the hypotenuse:

If we assume 8 is the hypotenuse, we use the sine function:

b = 8sin(30°) = 8 * 0.5 = 4

Thus, to solve for b, the appropriate equation to use is:

8sin(30°)

Using 8tan(30°) would be applicable if we were dealing with opposite and adjacent sides instead, but without additional context, 8sin(30°) is the clearer choice for this scenario.