Question

A ship is traveling around the outside rim of an island surveying a good place to land. If it is 10 miles from a lighthouse at the center of the island and 45° from due north, how far has the ship traveled from the most northern tip of the island to the nearest tenth

Answer 1

Answer: The ship traveled 14.14 miles from the most northern tip of the island.

Step-by-step explanation:

Since we have given that

Length of lighthouse from the island = 10 miles

Angle made due north = 45°

Consider, ΔABC,

$sin 45^\circ=\dfrac{AB}{AC}\\\\\dfrac{1}{\sqrt{2}}=\dfrac{10}{AC}\\\\AC=10\sqrt{2}=14.14\ miles$

Hence, the ship traveled 14.14 miles from the most northern tip of the island.

Answer 2

Sin 45 = x/10
x = 10 sin 45
so, x= 7.1 or 7 miles toward north.