Calculate crd120 crd150 crd165 and crd172 using Hipparchu

Calculate crd(120° ), crd(150°), crd(165°), and crd(172 ½ °) using Hipparchus’s formula for crd(180° - a)

Solution

We first need to calculate crd 120

. We get crd 120 = (4R² R²⁾ = 3R = 3 · 60 = 103; 55, 23.

Then the half-angle formula gives crd 30 = (R(2R crd 120)) = 31; 03, 30.

crd 150 = (4R² crd²30) = 115; 54, 40,

so crd 15 = (R(2R crd 150) )= 15; 39, 47.

Similarly, crd 165 = 118; 58, 25 and crd 71 2 = 7; 50, 54