a pole of 50m high stand on a building of 250m high to an observer of at a height of 300 m, the building and the pole stands equal angles. what the distance of the obsrever from the top of the pole

Not sure what you are saying here.

When you say the building and the pole are at equal angles, do you mean the top of the building, or the bottom? The top of the pole, or the bottom?

25 root 6 i'm sure

To find the distance of the observer from the top of the pole, we can use the concept of similar triangles. Here's the step-by-step explanation:

1. Draw a diagram representing the situation described in the question. Label the heights and angles involved.

2. Consider the smaller right triangle formed by the observer, the building, and the part of the pole above the building.

3. In this right triangle, the ratio of the height of the building to the distance of the observer from the building is equal to the tangent of the angle of elevation between the observer and the top of the pole.

tan(angle) = height of building / distance of observer from building

Rearrange the equation to find the distance of the observer from the building:

distance of observer from building = height of building / tan(angle)

4. Similarly, consider the larger right triangle formed by the observer, the building, and the entire pole.

5. In this right triangle, the ratio of the total height of the building and pole to the distance of the observer from the building is equal to the tangent of the equal angle of elevation between the observer and the pole.

tan(angle) = (height of building + height of pole) / distance of observer from building

Since the angles are equal, we use the same angle as before.

Rearrange the equation to find the distance of the observer from the top of the pole:

distance of observer from top of pole = (height of building + height of pole) / tan(angle)

6. Substitute the given values into the equations. Given: height of building = 250m, height of pole = 50m, height of observer = 300m, and equal angles.

distance of observer from building = 250m / tan(angle)
distance of observer from top of pole = (250m + 50m) / tan(angle)

7. Calculate the angles using the given information. If the building and the pole stand equal angles to the observer, then the angles are the same. Find the angle by using the inverse tangent function:

angle = arctan(height of building / height of observer)
angle = arctan(250m / 300m)

Calculate angle using a calculator, which gives us approximately 39.81 degrees.

8. Substitute the angle value into the distance equations:

distance of observer from building = 250m / tan(39.81 degrees)
distance of observer from top of pole = (250m + 50m) / tan(39.81 degrees)

9. Calculate the distances using a calculator to get the final answers. The distance of the observer from the building is approximately 391.37m, and the distance of the observer from the top of the pole is approximately 438.63m.

Therefore, the distance of the observer from the top of the pole is approximately 438.63m.