Question

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

Answer 1

Answer:

$AB \approx 4.054$

Step-by-step 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 $AB \approx 4.054$.