Regular Spherical Heptagons

Given that,

Number of sides of regular spherical heptagon, $n=7$ , arc length of side $a=6 cm$ , radius of spherical surface, $R=15 cm$

Now, using HCR's formula for regular spherical polygon

$\Large{\sin\left(\frac{\theta}{2}\right)\cos\left(\frac{a}{2R}\right)\sec\left(\frac{\pi}{n}\right)=1}$

$\implies \theta=2\sin^{-1}\left(\frac{1}{\Large{\cos\left(\frac{a}{2R}\right)\sec\left(\frac{\pi}{n}\right)}}\right)$

Substituting the corresponding values, the interior angle $\theta$ of regular spherical heptagon is given as

$\theta=2\sin^{-1}\left(\frac{1}{\Large{\cos\left(\frac{6}{2\times 15}\right)\sec\left(\frac{\pi}{7}\right)}}\right)=2\sin^{-1}\left(\frac{1}{\Large{\cos\left(\frac{1}{5}\right)\sec\left(\frac{\pi}{7}\right)}}\right)\approx 133.646038^{\circ}$