Towers A and B are on the east-west line 125 m apart. Jojo, on the north of that line finds that the direction of towers A and B are N 39deg27mins E and N 50deg33mins W, respectively. How far is Jojo from each tower?

I cannot make any sense of your description.

Jojo would have to be on the south side of line AB
Check it please

Assuming that north was a typo, leaving Jojo on the south side of AB,

Let Jojo be h mi S of the line AB.

h tan 50°33' + h tan 39°27' = 125
1.215h + 0.823h = 125
h = 125/2.038 = 61.335 mi

Now, letting b be the distance from B, and a that from A,

b = h/cos 50°33' = 61.335/0.635 = 96.59 mi
a = h/cos 39°27' = 61.335/0.772 = 79.45 mi

To find the distance of Jojo from each tower, we can use the concept of trigonometry and the given information about the directions of the towers.

Let's consider Jojo's position as point O, Tower A as point A, and Tower B as point B. We know that the distance between Towers A and B (AB) is 125 meters, and the directions of the towers are given as N 39° 27' E and N 50° 33' W, respectively.

To find the distance of Jojo from Tower A (OA), we can draw a right-angled triangle where the hypotenuse is AB (125m), and angle AOB is 90°.

First, we need to convert the given directions into decimal degrees.

N 39° 27' E can be written as 39.45° (since 27 minutes is 27/60 = 0.45 degrees).
N 50° 33' W can be written as -50.55° (since it is in the west, we use a negative sign and 33 minutes is 33/60 = 0.55 degrees).

Now, we can determine the angle BOA using the given directions:

Angle BOA = angle AOB = (180° - angle A - angle B) = (180° - 39.45° - (-50.55°)) = 180° + 39.45° + 50.55° = 270°.

Since we now have a right-angled triangle (AOB) with the angle BOA as 270°, we can use trigonometric functions.

In a right-angled triangle, the tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle:

tan(BOA) = (OA / AB).

Plugging in the known values, we have:

tan(270°) = (OA / 125).

Since the tangent of 270° is undefined, we can consider the complementary angle, which is 90°. Therefore:

tan(90°) = (OA / 125).

The tangent of 90° is equal to 1, so we have:

1 = (OA / 125).

Solving for OA:

OA = 1 * 125 = 125 meters.

Thus, Jojo is 125 meters away from Tower A.

To find the distance of Jojo from Tower B (OB), we can use the same method. Since we already have the angle BOA as 270°, we can use the complementary angle, which is 90°.

tan(90°) = (OB / 125).

Again, the tangent of 90° is equal to 1:

1 = (OB / 125).

Solving for OB:

OB = 1 * 125 = 125 meters.

Hence, Jojo is also 125 meters away from Tower B.

Therefore, Jojo is 125 meters away from each tower.