Two airplanes leave an airport at the same time An hour late

Two airplanes leave an airport at the same time. An hour later, the planes are 195km apart. If one plane has traveled 159km and the other has traveled 252km during the hour, find the angle theta between their flight paths. See the figure below. Carry your intermediate computations to at least four decimal places. Round your answer to the nearest tenth of a degree.

Solution

We will use law of cosine here which is

a^2=b^2 + c^2 - 2bc cos A

Here a= 195km , b=252km ,c=159km

195^2= 252^2 + 159^2 -2(252)(159)cos A

38025= 63504 + 25281 - 80136 cos A

80136 cos A= 50760

cos A= 50760/80136

A= cos^-1(50760/80136) = 50.7 degree