The first leg of the flight is (!.5 hr)(680 mph) = 1020 miles long. Let's call this side b of our triangle.

The second leg of the flight is (2 hr)(680 mph) = 1360 miles long. Let's call this side c of our triangle.

We can find the length of side a of the triangle from the law of cosines. The angle A between the two sides whose length we know is 170°. (180° - 10° = 170°).

a^{2} = b^{2} + c^{2} - (2)*(a)*(b)*cos(A)

a^{2} = (1020 miles)^{2} + (1360 miles)^{2} - (2)*(1020 miles)(1360 miles)*cos(170°)

a^{2} = 1040400 miles^{2} + 1849600 miles^{2} - (2774400 miles^{2})*cos(170°)

cos(170°) = -0.9848

a^{2} = 2890000 miles^{2} + 2732251 miles^{2} = 5622250.6 miles^{2}

**a** = (5622250.6 miles^{2})^{½} = **2371 miles**