Trigonometry
posted by Paul .
a flagpole 25 feet tall stands on a top of a building. from a point in the same horizontal plane with the base of the building. The angle of elevation of the top and the bottom are 61°30' and 56°20' respectively. How high is the building?

Draw a picture of the situation:
1.Draw ver. line AC with A on the bottom.
2. Add point D on line AC.
3. Draw a hor. line from A to the left.
Label it AB. Now we have a rt angle.
4. Draw hyp. BC.
5. Draw hyp. BD.
<ABC = <ABD + <DBC = 61.5o
56.33 + <DBC = 61.5
<DBC = 5.17o
<ACB = 180(61.5+90) = 28.5o
<BDC = 180(28.5+5.17) = 146.33o
sin5.17/25 = sin146.33/BC
BC = 153.8 Ft.
sin61.5 = (25+h)/153.8
h = 110 Ft. = Ht. of Bldg.