The boat shown in the accompanying figure is 3 miles from both lighthouses and the angle between the line of sight is 20 degrees. Find the distance between the lighthouses

Accepted Solution

Answer: [tex]1.04\ miles[/tex]Step-by-step explanation: Observe the figure attached. You can identify that the triangle formed is Isosceles, because it has  two equal sides. Notice that you can divide it into two equal right triangles. Now the angle 20° is divided by 2 and you get two equal angles that measure 10°. To find "x", apply the Trigonometric Identity [tex]sin\alpha=\frac{opposite}{hypotenuse}[/tex]:  [tex]sin(10\°)=\frac{x}{3}\\\\x=3*sin(10\°)\\\\x=0.52\ miles[/tex] Then, the distance between the lighthouses can be represented with: [tex]d=2x[/tex] Substituting the value of "x" into this equation, you get: [tex]d=2(0.52\ miles)\\\\d=1.04\ miles[/tex]