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

Answer:

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

Step-by-step 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;

$\dfrac{a}{sin(A)} = \dfrac{b}{sin(B)} = \dfrac{c}{sin(C)}$

Therefore, we have;

$\dfrac{5}{sin(70^{\circ})} = \dfrac{The \ distance \ from \ the \ ship \ to \ the \ dock}{sin(80^{\circ})}$

$\therefore The \ distance \ from \ the \ ship \ to \ the \ dock = sin(80^{\circ}) \times \dfrac{5}{sin(70^{\circ})}$

$sin(80^{\circ}) \times \dfrac{5}{sin(70^{\circ})} \approx 5.24 \ mi$

Therefore;

The distance from the ship to the dock ≈ 5.24 miles