Hello, redeemys24!

An astronomical object has an actual diameter of 128 km

and an apparent size of 24'16" as viewed from earth.

How far is this object from earth?

So, I converted into DD format and got

Your diagram is correct.

Bisect the vertex angle of that isosceles triangle.

You will have a right triangle.

One side runs from earth (E) to the center of the object (C).

. . Let

From the center directly to the right, CA is the radius of the object: 64 km.

. . And EA is the hypotenuse.

Let

We have: .

Hence: .