Question

As a ship approaches the dock, it forms a 70 angle between the dock and the lighthouse. At the lighthouse, an 80 angle is formed between the dock and the ship. How far is the ship from the dock?

Answer 1

The distance from the ship to the dock is approximately 5.24 miles

Explanation:

From the parameters given in the question, we have;

The angle formed between the dock and the lighthouse = 70°

The angle formed between the dock and the lighthouse at the ship = 80°

The distance between dock and the lighthouse = 5 miles (From a similar question online)

By sine rule, we have;

`(a)/(sin(A)) = (b)/(sin(B)) = (c)/(sin(C))`

Therefore, we have;

`(5)/(sin(70^(\circ))) = (The \ distance \ from \ the \ ship \ to \ the \ dock)/(sin(80^(\circ)))`

`\therefore The \ distance \ from \ the \ ship \ to \ the \ dock = sin(80^(\circ)) * (5)/(sin(70^(\circ)))`

`sin(80^(\circ)) * (5)/(sin(70^(\circ))) \approx 5.24 \ mi`

Therefore;

The distance from the ship to the dock ≈ 5.24 miles