Chapter 2 - Acute Angles and Right Triangles - Section 2.5 Further Applications of Right Triangles - 2.5 Exercises - Page 81: 17

$x\approx 47.4342 mi$

1. $\angle CAB = \angle NAB - \angle NAC$$= 130^{\circ} -40 ^{\circ} = 90 ^{\circ}$ $d(AC) = 1.5 hr\times18 knots = 27 miles $ $d(AB) = 1.5 hr\times26 knots = 39 miles $ 2. By Pythagorus theorem $x^2 = 27^2 +39^2$ $x = \sqrt {729+1521} \approx 47.4342 miles$