Question

A mountain is seen in a direction 30° north of east and is known to be 5 miles away from another mountain as seen in a direction 40° north of east 8 mile distance. how far apart are the two?

Answer 1

Answer on Question #77611 – Math – Trigonometry

Question

A mountain is seen in a direction $30{}^{\circ}$ north of east and is known to be 5 miles away from another mountain as seen in a direction $40{}^{\circ}$ north of east 8 mile distance. how far apart are the two?

Solution

$$\cos 30{}^{\circ} = \frac{\sqrt{3}}{2} = \frac{x}{5}; \quad x = 2.5\sqrt{3}$$ $$\sin 30{}^{\circ} = \frac{1}{2} = \frac{k}{5}; \quad k = 2.5$$ $$\cos 40{}^{\circ} = 0.77 = \frac{z}{8}; \quad z = 6.16$$ $$\sin 40{}^{\circ} = 0.64 = \frac{v}{8}; \quad v = 5.12$$ $$z - x = y; \quad y = 1.83$$ $$v - k = f; \quad f = 2.62$$ $$r = M1M2 = \sqrt{y^2 + f^2} = 3.2 \text{ miles}$$

**Answer**: $r = 3.2$ miles

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