Question

Any Einstein to solve this question?
A tower and a building stands on the same horizontal level from the midpoint P. The angle of elevation of e top T of e tower is 65 degrees. From the top Q of the Building, the angle of elevation from point P is 35degree. If the building is 20m high. Calculate,
A.The distance PT
B.The distance QT
C.The height of the tower

Answer 1

Answer:

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)

please mars as brainlist