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