from the top of 90 meters high building it is observe that the top of another building make a 40 degree angle depression. if two buildings 75 meters apart how tall is the other building?

Draw a diagram. If the top of the 90m tower is A, the top of the shorter building is B, draw a horizontal line from B to the 90m tower. Label the intersection C.

Now, ABC is a right triangle, and angle A is 45°. The difference in heights is side b. The distance between the buildings is a.

a/b = tan 50° = 1.192
b = 75/1.192 = 62.92m

So, the shorter building is 90-62.92 = 27.08m tall.

oops A is 50° (90° - angle of depression)

To find the height of the other building, we can use trigonometry and the given information:

Let's denote the height of the other building as h.

We know that from the top of the 90-meter-high building, the top of the other building forms a 40-degree angle of depression.

Now, let's use trigonometry. We can use the tangent function because we have the angle of depression and the opposite side length.

In this case, the opposite side to the angle of depression is the difference in height between the two buildings.

So, we can write the equation as:

tan(40 degrees) = (height of other building) / (distance between the buildings)

tan(40 degrees) = h / 75 meters

To solve for h, we multiply both sides by 75:

h = 75 * tan(40 degrees)

Using a calculator, multiply 75 by the tangent of 40 degrees, which equals approximately 57.66 meters.

Therefore, the height of the other building is approximately 57.66 meters.

To find the height of the other building, we can use trigonometry. Specifically, we can use the tangent function to relate the angle of depression to the height and distance.

Let's denote the height of the other building as "h."

Given:
Height of the observer's building = 90 meters
Angle of depression = 40 degrees
Distance between the two buildings = 75 meters

We can set up a right triangle to represent this situation. The side opposite the angle of depression is the height of the other building (h), the side adjacent to the angle is the distance between the buildings (75 meters), and the side opposite the right angle is the difference in height between the two buildings (90 meters - h).

Now, let's apply the tangent function:

tan(angle) = opposite / adjacent

tan(40 degrees) = (90 - h) / 75

To find "h," we can rearrange the equation:

h = 90 - 75 * tan(40 degrees)

Now we can calculate the value of "h" using a scientific calculator or trigonometric tables:

h ≈ 90 - 75 * 0.8391
h ≈ 90 - 62.93
h ≈ 27.07

Therefore, the height of the other building is approximately 27.07 meters.