Which equation can be used to solve for b?
tan(30°) = 5/b
tan(30°) = b/5
tan(30°) = 10/b
tan(30°) = b/10

Solution:

The right-angled triangle of the problem statement is presented below

Trigonometric relations are applied to right-angled triangles and the basic relations are summarised as follows.

sinθ = Perpendicular/Hypotenuse

cosθ = Base/Hypotenuse

The perpendicular is that side of the triangle which is opposite the angle θ. The base and hypotenuse contain the angle θ.

tanθ = Perpendicular/Base = Perpendicular/Hypotenuse × Hypotenuse/Base = sinθ × 1/cosθ

So coming back to the given right angled triangle we have:

tan 30° = 5/b

sin 30° = 1/2

cos 30° = √3/2

tan 30° = sin 30°/cos 30°

= 1/2 / √3/2

= 1 / √3

tan 30° = 5/b

1/√3 = 5/b

b = 5√3

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Which equation can be used to solve for b?

Summary:

The equation that can be used to solve for b is tan 30° = 5/b.