Question

Angle A is circumscribed about circle O what is the length of AB

Answer 1

`AB \approx 4.054`

Explanation:

The trigonometric equations associated with the figure are, respectively:

`AB = 4\cdot \cos 73^(\circ) + 3\cdot \cos \alpha`

`4\cdot \sin 73^(\circ) = 3 +3\cdot \sin \alpha`

The components with the unknown angle are cleared and used in the fundamental trigonometric relation:

`3\cdot \cos \alpha = AB - 4\cdot \cos 73^(\circ)`

`3\cdot \sin \alpha = 4\cdot \sin 73^(\circ) - 3`

`9\cdot \cos^(2)\alpha + 9\cdot \sin^(2)\alpha =(AB-4\cdot \cos 73^(\circ))^(2)+(4\cdot \sin 73^(\circ)-3)^(2)`

`9 = AB^(2)-2.339\cdot AB + 1.368 + 0.681`

The following second-order polynomial is presented below:

`AB^(2)-2.339\cdot AB -6.951 = 0`

Roots of the polynomial are described hereafter:

`AB_(1) \approx 4.054` and
`AB_(2) \approx -1.715`

Only the first root is reasonable, as length is a positive variable. The length is
`AB \approx 4.054`.