Find height & distance of the second building.

[greatwhiteshark]

From the top of a building 50 feet high the angles of elevation and depression of the top and bottom of another building are 19° 41' and 26° 34', respectively. What are the height and distance of the second building.

 

[soroban]

Hello, greatwhiteshark!

From the top of a building 50 feet high the angles of elevation and depression
of the top and bottom of another building are 19° 41' and 26° 34', respectively.
What are the height and distance of the second building?

                    *C         AB is the 50-foot building.
                 *  |
              *     |y         Angle CAE = 19 deg.41 minutes.
           *        |          Angle EAD = 26 deg.34 minutes.
        * 19d41'    |
    A* - - - - - - -+E         AB = ED = 50 
     |  * 26d34'    |
     |     *        |          BD = AE = x
  50 |        *     |50
     |           *  |          CE = y
 - - * - - - - - -  *
     B      x       D

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
In right triangle AED: . tan(26^o34') .= .----
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
. . . . . . . . . . . . . . 50
Hence: . x .= .-------------- .= .99.99295 .≈ .100 feet . (distance)
. . . . . . . . . . . tan(26^o34')

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .y
In right triangle CEA: . tan(19^o41') .= .------
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .100

Hence: . y .= .100 tan(19^o41') .= .35.7723...

Therefore: . 50 + 35.8 .= .85.8 feet . (height)

 

[greatwhiteshark]

okay

Like always, your explanations are divine.