Answer to Question #133703 in Trigonometry for GRACE

Question

A PLDT Tower and a monument stand on a level plane.
The angles of depression of the top and bottom of the
monument viewed from the top of the PLDT Tower is 13
degrees and 35 degrees respectively. The height of the
tower is 50m. Find the height of the monument.

Answer 1

Find the side $BC$:

$tan\angle EBC=\frac{CE}{BC}$

$tan 35\degree=\frac{50}{BC}$

$BC=\frac{50}{tan 35\degree}$

$BC=\frac{50}{0.70}$

$BC=71.43$

Then find the side $CD$:

$tan \angle CBD=\frac{CD}{BC}$

$CD=BC⋅tan 13\degree$

$CD=71.43⋅0.23$

$CD=16.43$

Therefore we have:

$DE=CE-CD=50-16.43=33.57$

Answer: The height of the monument is $33.57$m.