I have no idea how to do this problem

From an airplane flying 2 kilometers aboce the ocean, a piolet sees two ships directly to the east. The angles of depression to the ships are 8 degrees 20 minutes and 75 degrees 40 minutes how far away are the ships?

I know what the anlge of depression is the only thing is that my teach told me the answer was 13.03 and I got like 3 something...

I don\'t think I know how to properly do this problem

Don't try these without a diagram.

Draw a straight line (the ocean) and mark two points A and B (the two ships)

put a point above that line and to the left of points A and B, name that point P for the plane.
Draw a perpendicular from P to the line containing A and B and call that point Q

You should now see two right angled triangles, PQA and PQB, with the right angle at Q
From the description angle PAQ = 8.33º and angle PBQ = 75.67º and PQ = 2

in the large triangle,
tan 8.33 = 2/QB
QB = 2/tan 8.33

in the smaller triangle
tan 75.67 = 2/QA
QA = 2/tan 75.67

so AB = QB - QA
= 2/tan 8.33 - 2/tan 75.67

Calculator time !

Let A be the angle of depression of a ship and let H be the altitude of the airplane.

The distance of each ship from the vertical below the airplane, measured at sea level, is
D = H/tan A
That distance is 13.65 miles for the ship with 8.333 degree depression angle, and 0.51 miles for the other ship. The distance BETWEEN the ships (which is not what you asked for) is 13.14 miles

The distance to the ships from the airplane is
H/(sin A1) = 13.80 km
H/(sin A2) = 2.06 km

You should now see two right angled triangles, PQA and PQB, with the right angle at Q

From the description angle PAQ = 8.33º and angle PBQ = 75.67º and PQ = 2

were did you get the angles from

I thought you could do

90 - 75 degrees 40 minutes to get the angle QPA but I got 14

The angle PAQ is the angle of elevation viewed from the ship, which is the same as the angle of depression viewed from the airplane (8&deg20'). The same for ship B.

This is because the angles of elevation and depression are alternate angles between two parallel lines.

I agree with the two calculations above using H/tan(θ) for the horizontal distance, and the answer of 13.143 km.

To solve this problem, you can use trigonometry, specifically the tangent function. Let's break down the problem step by step:

1. Draw a diagram: Draw a diagram representing the situation described. Label the airplane as A, the two ships as S1 and S2, and the ocean surface as O. Draw a line segment from A to each ship, representing the line of sight.

2. Identify given information: The problem states that the airplane is flying 2 kilometers above the ocean surface. It also provides the angles of depression to the two ships: 8 degrees 20 minutes and 75 degrees 40 minutes.

3. Define the tangent function: The tangent of an angle can be defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side will be the height of the airplane above the ocean, and the adjacent side will be the horizontal distance to each ship.

4. Set up equations: Let's define the variables:
- d1: the horizontal distance from the airplane to ship S1.
- d2: the horizontal distance from the airplane to ship S2.
- h: the height of the airplane above the ocean (2 kilometers or 2000 meters).

Using the tangent function, we can set up the following equations:
- tan(angle of depression to S1) = h / d1
- tan(angle of depression to S2) = h / d2

5. Convert degrees and minutes to decimal form: To use trigonometric functions, we need angles in decimal form. Convert the angles of depression to decimal degrees. For example, 8 degrees 20 minutes is approximately 8.33 degrees, and 75 degrees 40 minutes is approximately 75.67 degrees.

6. Solve the equations: Substitute the decimal values into the equations you set up in step 4. Solve for d1 and d2.

- For example, let's say we have:
- angle of depression to S1 = 8.33 degrees
- angle of depression to S2 = 75.67 degrees
- h = 2000 meters

Using the equations: tan(8.33 degrees) = 2000 / d1 and tan(75.67 degrees) = 2000 / d2, solve for d1 and d2.

7. Calculate the distances to the ships: Once you have the values of d1 and d2, you can calculate the horizontal distances from the airplane to ships S1 and S2.

8. Compare your answer: Compare your calculated distances to the answer provided by your teacher (13.03 kilometers). If they are significantly different, review your calculations and check for any errors in rounding or unit conversion.

Remember to check that your calculator is set to the correct angle measurement mode (degrees or radians) and units (meters or kilometers) to avoid calculation errors.

Following these steps should help you solve the problem correctly.