You need to know how far you are away from the lighthouse. You use a range finder to find the distance from the sailboat to the lighthouse light is 245 yards.
For angle B, chose an angle measure between 25° and 45°: _
Based on the above information, find the distance from the sailboat to the island where the lighthouse is located.

The distance from the sailboat to the island where the lighthouse is located is approximately 212.2 yards

Step-by-step explanation:

The distance between the sailboat and the lighthouse is found using trigonometric ratios as follows;

The given parameters are;

The distance from the sailboat to the lighthouse's light = 245 yards

The angle of elevation of angle B = An angle chosen between 25° and 45°

For simplicity, we chose, B = 30°

A right triangle formed with the height of the light house and the horizontal distance of the sailboat from the lighthouse as legs and angle B is the angle adjacent to the horizontal distance of sailboat from the light house

The hypotenuse length = The distance from the sailboat to the lighthouse's light = 245 yards

By trigonometric ratio, in the we have;

The adjacent leg length = The horizontal distance of sailboat from the light house

The horizontal distance between the sailboat and the light house = 245 × cos(30°) ≈ 212.176223927

Therefore;

The horizontal distance between the sailboat and the lighthouse ≈ 212.2 yards

Therefore, the distance from the sailboat to the island where the lighthouse is located ≈ 212.2 yards.

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