Question

You need to know how far you are away from the lighthouse.

Answer 1

Answer:

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;

$cos\angle B = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}$

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

$\therefore cos (30^{\circ}) = \dfrac{The \ horizontal \ distance \ between \ the \ sailboat \ and \ the \ lighthouse }{245 \ yards}$

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.