Question #133703
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.
1
Expert's answer
2020-09-19T13:04:07-0400


Find the side BCBC:

tanEBC=CEBCtan\angle EBC=\frac{CE}{BC}

tan35°=50BCtan 35\degree=\frac{50}{BC}

BC=50tan35°BC=\frac{50}{tan 35\degree}

BC=500.70BC=\frac{50}{0.70}

BC=71.43BC=71.43

Then find the side CDCD:

tanCBD=CDBCtan \angle CBD=\frac{CD}{BC}

CD=BCtan13°CD=BC⋅tan 13\degree

CD=71.430.23CD=71.43⋅0.23

CD=16.43CD=16.43

Therefore we have:

DE=CECD=5016.43=33.57DE=CE-CD=50-16.43=33.57

Answer: The height of the monument is 33.5733.57m.







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