Question

Two airplanes leave an airport At the same time. An hour later, the planes are 230 km apart. If one plane has arrived 199km and the other has traveled 154 km during the hour, find the angle 0 between their flight paths. See the figure below. Carry your intermediate computations to at least 4 decimal places. Round your answer to the nearest tenth of a degree.

Answer 1

Given:

`a=154\text{ }km,\text{ }b=230\text{ }km,\text{ }c=199\text{ }km,\text{ and }\angle B=\theta.`

Required:

We need to find the measure of the angle.

Step-by-step explanation:

Consider the cosine law.

`b^2=a^2+c^2-2ac\text{ }cosB`
`-(b^2-a^2-c^2)/(2ac)=cosB`
`cosB=(a^2+c^2-b^2)/(2ac)`
`Substitute\text{ }a=154\text{ }km,\text{ }b=230\text{ }km,\text{ }c=199\text{ }km,\text{ and }\angle B=\theta\text{ in the equation.}`
`cos\theta=0.6039`
`\theta=52.8493\degree`
`\theta=52.8\degree`

Final answer:

`\theta=52.8\degree`