Dibuja un diagrama para ayudarte a visualizar el problema.Right triangle, C,P,R, horizontal leg, PR, labeled, 5, vertical leg, CP, labeled, r, angle, C, labeled theta. hypotenuse, CP, labeled, R, +, x. Point on side, CR, labeled, Q, & segment, QR, labeled, x.

$θ = 360° – 314°$
$θ = 46°$Added to the triangle, angle c, labeled, 46 degrees.

Dibuja un diagrama para ayudarte a visualizar el problema.Added to circle, segments from the center, to the end points of the chord, with dashed segment from center, perpendicular to the chord, creating 2 right triangles. Each radii labeled, 7 units, each central angle for the right angles, labeled theta.

$θ = 102° \times 1/2$
$θ = 51°$Angles labeled theta, changed to label, 51 degrees.

$\text{tan}(46^{\circ})=\frac{5}{r}$

$r=\frac{5}{\text{tan}(46^{\circ})}$

r ≈ 4.83

$\text{sen}(46^{\circ})=\frac{5}{4.83+x}$

$4.83+x=\frac{5}{\text{sen}(46^{\circ})}$

x ≈ 6.95 – 4.83

$\text{sen}(51^{\circ})=\frac{\frac{x}{2}}{7}$

$\frac{x}{2}=7\text{sen}(51^{\circ})$

$x = 14\text{ sen}\left(51°\right)$

$QR ≈ 2.12$

$x ≈ 10.88 \text{ unidades}$