A small plane takes off from island A and flies in a straight line for 12 kilometers. At the same time, a sailor sitting in a sailboat who is 5 miles from the island measures the angled by from island A to the sailboat and the plane is 37 degrees. How far is the plane from island B? Please draw and label the situation if possible.

Question

A small plane takes off from island A and flies in a straight line for 12 kilometers. At the same time, a sailor sitting in a sailboat who is 5 miles from the island measures the angled by from island A to the sailboat and the plane is 37 degrees. How far is the plane from island B? Please draw and label the situation if possible.

Answer 1

I have no idea where the sailor is.

Answer 2

or island B

Answer 3

This same post has been declared as muddled and garbled several times.

It has been answered by both Steve and I and you should not expect any more replies until you fix the wording so that the question makes sense

http://www.jiskha.com/display.cgi?id=1460596777

Answer 4

To solve this problem, we can use trigonometry, specifically trigonometric functions such as sine, cosine, and tangent.

Let's label the points. We have island A, the sailboat, the plane, and island B. Let's call the distance from island A to the sailboat "x" (which is 5 miles or 8 kilometers), and let's call the distance from island A to island B "d."

Based on the information given, we know that the angle between the line connecting the plane and the sailboat and the line connecting the sailboat and island B is 37 degrees.

Now, let's draw a diagram to visualize the situation:

A-----------------B
|
|
|
P
/
/
/
S

In this diagram, A represents island A, B represents island B, P represents the plane, and S represents the sailboat. The angle marked between S and P is 37 degrees.

We can use the tangent function to solve this problem. The tangent of an angle is equal to the length of the opposite side divided by the length of the adjacent side.

In this case, the opposite side is the distance between the plane and the sailboat, which is x (5 miles or 8 kilometers), and the adjacent side is the distance between the plane and island B, which is d (what we want to find).

So, we have the equation:

tangent(37 degrees) = x/d

Now, we can solve for d:

d = x / tangent(37 degrees)

Using a calculator, we can find the value of tangent(37 degrees) is approximately 0.7536.

So, substituting the values:

d = x / 0.7536

d = 8 km / 0.7536

d ≈ 10.62 kilometers (rounded to two decimal places)

Therefore, the plane is approximately 10.62 kilometers away from island B.