Question

Without using a trigonometric ratio, find the distance from the ship to the buoy, B. Round the distance to the nearest tenth of a mile.

Answer 1

Without using the trigonometry ratio, we can find the distance between the ship and the buoy by:

the distance between City and Lemont SUBTRACT the vertical distance between City and the point parallel to the Ship

The distance between the City and Lemont can be worked out using the Sin rule 
$\frac{57.8}{sin(36)}= \frac{City-Lemont}{sin(92)}$
$City-Lemont= \frac{57.9sin(92)}{sin(36)} = 98.27.....$≈98.3

The vertical distance between the City and the point parallel to the ship can be worked out using the Pythagoras theorem
$\sqrt{57.8^{2}- 44.6^{2} } =36.765...$≈36.8

The distance between the ship and the Buoy is given:
$98.3-36.8=61.5$ miles