From the top of a building the angle of elevation of the top of a nearby building is 23 degrees and the angle of depression of the bottom of the nearby building is 52 degrees. The distance between the two buildings is 35m. What is the height of the second building?

tan 23 = top part /35

so top part = 35 tan 23

tan 52 = bottom part/35
so bottom part = 35 tan 52

so top part + bottom part = total height = 35(tan 23 +tan 52)

oh well :)

or, using the law of cosines,

h^2 = (35sec23°)^2 + (35sec52°)^2 - 2(35sec23°)(35sec52°)cos75°

Now, isn't that nice and simple? ...

To find the height of the second building, we can use trigonometry. We will use the tangent function to calculate the height.

Let's label the angles and sides of the right triangle formed by the two buildings.

In the first triangle:
Angle of elevation = 23 degrees
Opposite side (height of second building) = h (unknown)

In the second triangle:
Angle of depression = 52 degrees
Adjacent side (distance between the buildings) = 35 m

By using the tangent function, we can set up the following equations:

In the first triangle:
tan(23) = h / 35

In the second triangle:
tan(52) = h / 35

Now we can solve for h by setting up and solving this system of equations.

First, let's find the value of h using the equation from the first triangle:
h / 35 = tan(23)

To isolate h, we can multiply both sides of the equation by 35:
h = 35 * tan(23)

Now, let's calculate the value of h using a calculator:
h ≈ 35 * 0.4245 ≈ 14.87 m

Therefore, the height of the second building is approximately 14.87 meters.

Nevermind, I found it..