Three towns a, b, and c are such that the distance between a and b is 50km and the distance between a and c is 90km. if the bearing of b from a is 075' and the bearing of c from a is 310'. find the distance between b and c?

I will assume you meant ° for degrees.

angles are measured in degrees, subdivided into 60 minutes, and then again into 60 seconds (just like "time" )

e.g. 34° 12' 35" <--- 34 degrees, 12 minutes, and 35 seconds

Make a sketch
From your description, I have a triangle ABC
with angle A = 125° , AB = 50 and AC = 90

using cosine law:
BC^2 = 50^2 + 90^2 - 2(50)(90)cos 125°
= 10600 - 9000(-.57357..)
= ...

finish it up

how did u solved it pls

291 Please how did you solve it and got the bearing as 291

Let me see the working

I want to see the diagram

To find the distance between towns b and c, we can use the Law of Cosines. The Law of Cosines states that, in a triangle with sides a, b, and c, and angle C opposite side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, we are interested in finding the distance between towns b and c, which will be our side c.

First, let's start by calculating the angle between towns b and c. We know the bearings of b from a and c from a, so we can use this information:

Bearing of b from a = 075' = 75 degrees
Bearing of c from a = 310' = 310 degrees

To find the angle between b and c, we subtract the bearing of c from the bearing of b:

Angle between b and c = 310 degrees - 75 degrees = 235 degrees

Now that we have the angle, we can apply the Law of Cosines to find the distance between b and c. Let's set up our equation:

Distance between b and c (side c)^2 = distance between a and b (side a)^2 + distance between a and c (side b)^2 - 2 * distance between a and b * distance between a and c * cos(angle between b and c)

Using the given distances:
c^2 = 50^2 + 90^2 - 2 * 50 * 90 * cos(235 degrees)

Now we can calculate the distance between b and c:

c^2 = 2500 + 8100 - 9000 * cos(235 degrees)

Calculating cos(235 degrees) = -0.42262

c^2 = 2500 + 8100 + 9000 * 0.42262

c^2 = 2500 + 8100 + 3808.58

c^2 = 14408.58

Taking the square root of both sides, we get:

c ≈ 120.02 km

Therefore, the distance between towns b and c is approximately 120.02 km.