# trigonometry

posted by john

A man standing 9m above the ground,observes the angle of elevation and depression of the top and bottom of Rizal monument in luneta as 6° 50' and 7° 30' respectively find the height of the monument

1. Reiny

Sketch the situation.
On my sketch, I labeled the top of the monument as A and its bottom as B, with B on ground level

I placed the man at a point 9 m above ground at some distance away from the monument and labeled that P
I drew a horizontal from P to meet AB at Q

I now have two right-angled triangles.
In triangle BPQ, BQ=9, angle BPQ = 7.5°
tan 7.5° = 9/PQ
PQ = 9/tan 7.5° = .....

in triangle APQ,
tan 6° 50' = AQ/PQ , but we know PQ

AQ = PQ(tan 6° 50') = ......

AB = 9 + AQ = .....

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