SOLUTION: A tower and a building stand on the same horizontal level. From the point (P) at the bottom of the building, the angle of elevation of the top (T) of the tower is 65•. From the top

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A tower and a building stand on the same horizontal level. From the point (P) at the bottom of the building, the angle of elevation of the top (T) of the tower is 65•. From the top      Log On

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Question 770333: A tower and a building stand on the same horizontal level. From the point (P) at the bottom of the building, the angle of elevation of the top (T) of the tower is 65•. From the top (Q) of the building the angle of elevation of the of the top (T) is 25•. If the building is 20m high, calculate the distance PT. Hence calculate the height of the tower...
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
RT=towerheight , PQ=20meters=buildingheight=SR, so ST=RT-SR=RT-20m
RT=towerheight and PT is what we we need to find.
We know the measures of all the angles in the sketch.
Right triangle PRT has a 65%5Eo angle,
so the other acute angle (angle PTS) measures 90%5Eo-65%5Eo=25%5Eo
Right triangle QST has a 25%5Eoangle,
so the other acute angle (angle QTS) measures 90%5Eo-25%5Eo=65%5Eo
Triangle PQT has obtuse angle PQT, measuring 90%5Eo%2B25%5Eo=115%5Eo.
It also has angle PTQ measuring QTS-PTS=65%5Eo-25%5Eo=40%5Eo.
Applying law of sines we get
PT%2Fsin%28PQT%29=PQ%2Fsin%28PTQ%29-->PT%2Fsin%28115%5Eo%29=%2820m%29%2Fsin%2840%5Eo%29
and since sin%28115%5Eo%29=sin%28180%5Eo-65%5Eo%29=sin%2865%5Eo%29,
PT%2Fsin%2865%5Eo%29=%2820m%29%2Fsin%2840%5Eo%29-->PT=%2820m%29%2Asin%2865%5Eo%29%2Fsin%2840%5Eo%29-->highlight%28PT=28.2m%29(rounded)
Then, from triangle PRT,
RT=PT%2Asin%2865%5Eo%29-->RT=about%2828.2m%29%2Asin%2865%5Eo%29-->highlight%28RT=25.6m%29(rounded)