Question

To measure the height of a building,two sightings are taken a distance of 50 feet apart. Of the first angle of elevation is 40 degrees and the second is 32 degrees, what is the height of the building?

Answer 1

Of course you made a diagram, right?
let's label A and B as the points where the two readings were taken, A being the 32 degree.
Let C be the base of the building and D the top of the building.
in triangle ABD , angle A = 32, angle ABD = 140 and angle ADB = 8
by sine law:
BD/sin32 = 50/sin8
BD = 50sin32/sin8 = 190.38

Now go back to the right-angled triangle BCD and use
sin 40 = DC/190.38

I am sure you can take it from here

Answer 2

sin9 degere