Question

Frank and Marie set sail from the same point. Frank is sailing in the direction S5 °E. Marie is sailing in the direction S9°W. After 3 hours, Marie was 2 miles due west of Frank. How far had Marie sailed? Round to 4 decimal places.

Answer 1

Answer on Question #67631 – Math – Trigonometry

Frank and Marie set sail from the same point. Frank is sailing in the direction S5 °E. Marie is sailing in the direction S9°W. After 3 hours, Marie was 2 miles due west of Frank. How far had Marie sailed? Round to 4 decimal places.

Solution

$a + b = 2$ (due to condition)

$a = 2 - b$

In triangle hypotenuse (I) is given by

$$\begin{array}{l} l = \frac{a}{\sin 9{}^{\circ}} = \frac{b}{\sin 5{}^{\circ}} \\ \frac{b}{0.087156} = \frac{2 - b}{0.156434} \end{array}$$

From this equation it follows that

$$0.156434 * b = 0.087156 * 2 - 0.087156 * b$$ $$0.24356 * b = 0.174321$$ $$b = 0.715595878$$ $$l = \frac{0.715595878}{0.087156} = 8.2105 \text{ (miles)}$$

**Answer:** 8.2105 miles.

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