Answer to Question #133443 in Trigonometry for Joseph Se

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 are 13 degrees and 35 degrees, respectively. The height of the tower is 50 meters. Find the height of the monument.

Answer 1

Draw a diagram.

$Triangle ABC:$

$\angle BAC= 13 \degree$

$\tan (\angle BAC) = \tan 13\degree = \dfrac{BC}{AB} = \dfrac{50-h}{z}$

$z = \dfrac{50-h}{\tan 13\degree}$

$h = 50 - \tan 13\degree*z$ $(1)$

$Triangle ABD:$

$\angle BAD= 35 \degree$

$\tan (\angle BAD) = \tan 35\degree = \dfrac{BD}{AB} = \dfrac{50}{z}$

$z = \dfrac{50}{\tan 35\degree}$ $(2)$

$Substitute (2) to (1):$

  $h = 50 - \tan 13\degree*\dfrac{50}{\tan 35\degree}$   

$h = 33.5 m$

Height of the house is 33.5 m