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