Find the side BCBCBC:
tan∠EBC=CEBCtan\angle EBC=\frac{CE}{BC}tan∠EBC=BCCE
tan35°=50BCtan 35\degree=\frac{50}{BC}tan35°=BC50
BC=50tan35°BC=\frac{50}{tan 35\degree}BC=tan35°50
BC=500.70BC=\frac{50}{0.70}BC=0.7050
BC=71.43BC=71.43BC=71.43
Then find the side CDCDCD:
tan∠CBD=CDBCtan \angle CBD=\frac{CD}{BC}tan∠CBD=BCCD
CD=BC⋅tan13°CD=BC⋅tan 13\degreeCD=BC⋅tan13°
CD=71.43⋅0.23CD=71.43⋅0.23CD=71.43⋅0.23
CD=16.43CD=16.43CD=16.43
Therefore we have:
DE=CE−CD=50−16.43=33.57DE=CE-CD=50-16.43=33.57DE=CE−CD=50−16.43=33.57
Answer: The height of the monument is 33.5733.5733.57m.
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