a ship at sea sighted at two lighthouses. A and B on shore. The lighthouse are 15 miles apart. the measure of the angle at A is 41.5 degree. the angle at B is 36 degree towards the ship. find the distance to the nearest tenth of a mile from A to the ship.
Make a sketch of triangle SAB where S is the position of the ship
So I get angle A = 41.5° and angle B = 36°, leaving angle S = 102.5°
You want SA
by the sine law:
SA/sin36 = 15/sin102.5°
SA = 15sin36/sin102.5 = ....
To solve this problem, we can use the concept of trigonometry. Let's consider the diagram as follows:
Ship
/
/
/
/ x
/ \
/ \
/ θ \
/_________\
Lighthouse A Lighthouse B
Now, using trigonometry, we can say that:
tan(θ) = x / 15
We know that the angle θ at B is 36 degrees towards the ship. So we have:
tan(36) = x / 15
Now we can solve for x by rearranging the equation:
x = 15 * tan(36)
Using a calculator to find the tangent of 36 degrees, we get:
x ≈ 10.47 miles
So, the distance from Lighthouse A to the ship is approximately 10.47 miles.