Question

You will need to use knowledge of the sine and cosine functions from the acronym SOHCAHTOA.A bearing is an acute angle relative to the North/South line on a compass. Some examples are demonstrated below. ( see link )Explain how to solve each problem thoroughly, along with a thoroughexplanation of the concepts used to solve each problem.1. A car leaves a city at a bearing of N 50◦ E and travels in a straight line for 200 miles. How many miles north and how many miles east has the car traveled from the city?

Answer 1

The above diagram shows this situation. We have to find the values of x and y

Definition of sine

`\sin (angle)=\frac{\text{opposite}}{\text{hypotenuse}}`

Applying this definition to the angle of 50°, and solving for x:

`\begin{gathered} \sin (50^o^{})=(x)/(200) \\ \sin (50^o)\cdot200=x \\ 153.21\approx x \end{gathered}`

Definition of cosine

`\cos (angle)=\frac{\text{adjacent}}{\text{hypotenuse}}`

Applying this definition to the angle of 50°, and solving for y:

`\begin{gathered} \cos (50^o)=(y)/(200) \\ \cos (50^o)\cdot200=y \\ 128.56\approx y \end{gathered}`

Answer: The car traveled 153.21 miles east and 128.56 miles north