Abuilding was created from two stories. from a point 87 feet from the base of the building, the angle of elevation to the top of the first floor is 25° and the angle of elevation to the top of the second floor is 40°. to the nearest tenth of a foot, what is the height of the second floor?

- We´re gonna work with two separate triangles:

-The first one is the larger triangle (40º angle) and a vertical side that represents the ENTIRE height, b, of the tower.

Larger triangle with height b: tan 40°= ; .8390996312 = ;  b≈73.00166791

-The second one the smaller triangle (25º angle) and a vertical side, a, that represents the height of the first (bottom) section of the tower.

Smaller triangle with height a: tan 25°= ; ..4663076582 = ;  a≈40.56876626

-Then you need to solve for the vertical heights (b and a) in the two separate triangles.

-The needed height, x, of the second (top) section of the tower will be the difference between the ENTIRE height, b, and the height of the first (bottom) section, a. You will need to subtract.

In both triangles, the solution deals with "opposite" and "adjacent" making it a tangent problem.

Difference (b - a): 73.00166791 - 40.56876626 = 32.43290165 ≈ 32 feet