Juan and Romella are standing at the sea shore 10 miles apart. The coastline is a straight line between them. Both can see the same ship in the water. The angle between the coastline and the line between the ship and Juan is 35 degrees. The angle between the coastline and the line between the ship and Romella is 45 degrees. How far is the ship from Juan?
A) 16.8 miles
B) 7.2 miles
C) 14.0 miles
We can solve this problem using trigonometry.
Let's call the distance from the ship to Juan "x". We can use the tangent function to find x:
tan(35) = (distance from ship to Juan) / 10
(distance from ship to Juan) = 10 * tan(35)
(distance from ship to Juan) ≈ 6.84 miles
Now, let's call the distance from the ship to Romella "y". We can use the tangent function again to find y:
tan(45) = (distance from ship to Romella) / 10
(distance from ship to Romella) = 10 * tan(45)
(distance from ship to Romella) ≈ 10 miles
We want to find the distance between Juan and the ship, which is the hypotenuse of a right triangle with sides x and 10. We can use the Pythagorean theorem to find this distance:
distance between Juan and ship = √(x^2 + 10^2)
distance between Juan and ship = √(6.84^2 + 10^2)
distance between Juan and ship ≈ 12.0 miles
Therefore, the answer is not one of the options provided. However, the closest option is C) 14.0 miles.