Fig. 12-6. Altitude Determination Geometry for CTS

Fig. 12-6. Altitude Determination Geometry for CTS

Applying Napier's rules to the right spherical triangles ETS, ERS, and QTS, the arc length SE is

}// = arc cos(S • E) = arc cos(cosfis cos Aa) ('2-31)

and the rotation angle, A, is

where PE = i) - 90° and the arc length, TQ, is 90 deg. Next, the quadrantal spherical triangle, QES, is solved for the angle ESQ-.

<&£= Z ESQ = arc cos(cos(90° - Aa)/sin (12-33)

Combining Eqs. (12-30), (12-32), and (12-33) with Z YSR = 90 deg gives the result

4>s = 90° -arcsin(sin^£/sin^)-arccos(sinAa/sin^) (12-34)

or where

= arc cos(siny3£/sin»i') — arc cos(sin Aa/sin^)

Finally, i2£ and PE are related through the quadrantal spherical triangle, YSE, by PE = arc cos(cos Ss cos Aa/cos K£) (12-37)

One problem with the geometric method is apparent from the proliferation of inverse trigonometric functions in Eqs. (12-31) to (12-37), which results in quadrant

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