A glider traveling at 80 miles per hour in the direction $\mathrm{N} 12 \cdot \mathrm{W}$ encounters a mild wind with speed 15 miles per hour. If the wind is traveling from east to west, find the resulting speed of the glider and its direction.
Select one:
a. The glider travels with the resulting speed 84.4 in the direction $\mathrm{S} 67.99^{\circ} \mathrm{W}$.
b. The glider travels with the resulting speed 84.4 in the direction $\mathrm{S} 22.01^{\circ} \mathrm{W}$.
c. The glider travels with the resulting speed 74.4 in the direction $S 22.01^{\circ} \mathrm{W}$.
d. The glider travels with the resulting speed 74.4 in the direction $\mathrm{N} 67.99^{\circ} \mathrm{W}$.
e. The glider travels with the resulting speed 84.4 in the direction $\mathrm{N} 22.01^{\circ} \mathrm{W}$.

Step 1 ：Break down the glider's velocity into its northward and westward components. The northward component is \(80\cos(12)\) and the westward component is \(80\sin(12)\).

Step 2 ：Calculate the northward and westward components of the glider's velocity: \(v_{\text{north glider}} = 78.25\) and \(v_{\text{west glider}} = 16.63\).

Step 3 ：The wind's velocity is entirely in the westward direction, so it adds to the glider's westward velocity. The wind's velocity is 15.

Step 4 ：Calculate the resulting northward and westward velocities: \(v_{\text{north result}} = v_{\text{north glider}} = 78.25\) and \(v_{\text{west result}} = v_{\text{west glider}} + v_{\text{wind}} = 31.63\).

Step 5 ：Calculate the resulting velocity of the glider using the Pythagorean theorem: \(v_{\text{result}} = \sqrt{v_{\text{north result}}^2 + v_{\text{west result}}^2} = 84.4\).

Step 6 ：Calculate the direction of the resulting velocity using the arctangent of the ratio of the westward component to the northward component: \(\text{direction result} = \arctan\left(\frac{v_{\text{west result}}}{v_{\text{north result}}}\right) = 22.01^\circ\).

Step 7 ：\(\boxed{\text{The glider travels with the resulting speed 84.4 in the direction } N 22.01^\circ W}\)