On the top of a high-rise building, there is a 15m flagpole. From point on the ground, a student sights the top and bottom of the 15m flagpole on the top of the building. The angle of elevation from the ground to the bottom of the flagpole is 57.3 degrees. The angle of elevation from the ground to the top of the flagpole is 64.6 degrees. How far is the student from the foot of the building.
Also i understand most of this just dont know how i'd draw it out either. It's two triangles in one i think.
2006-12-03 11:42:10 · 4 answers · asked by shitheadjulie1 1 in Science & Mathematics ➔ Mathematics
You are right, it's two triangles in one (which actually makes three triangles).
The bottom triangle has angles of 57.3 at the ground and 33.7 at the bottom of the pole. The entire triangle has angles of 64.6 at the ground and 25.4 at the top of the pole. There is a skinny little triangle also which is where you start. It has an angle of (64.6 - 57.3) or 7.3 at the bottom and shares the 25.4 angle at the top, and it has a side of 15 m. Find the side of the skinny triangle which is also the hypotenuse of the bottom triangle using the Law of Sines. Then use that to find the bottom of the triangle using either sine law or just cosine (cos = adj/hyp). Feel free to IM if that's not enough explanation.
2006-12-03 12:23:18 · answer #1 · answered by hayharbr 7 · 0⤊ 0⤋
You need to draw a diagram with two right triangles. Both triangles have a base from a point on the ground to the base of the building. We will call that distance x. There is a right angle at the point where the ground meets the base of the building. Let the distance from the base of the building to the bottom of the flagpole be y. The distance from the base of the building to the top of the flagpole is y+15.
The first triangle then has base x and height y and an angle of v=57.3 degrees from the ground to the bottom of the flagpole.
tan v = y/x
The second triangle then has base x and height y+15 and an angle of w=64.6 degrees from the ground to the bottom of the flagpole.
tan w = (y+15)/x
We need to solve for x.
Multiplying both equations by x we get.
x*tan v = y
x*tan w = y+15
or x*(tan w) - 15 = y
So x*tan v = x*(tan w) - 15
Grouping the x terms we get
x*[(tan w) - (tan v)] = 15
Solving for x we get
x = 15 / [(tan w) - (tan v)] = 15 / [(tan 64.6) - (tan 57.3)]
x = 27.36 m
2006-12-03 21:55:20 · answer #2 · answered by Northstar 7 · 0⤊ 0⤋
Changing the angle from 57.3º to 64.6º increases the height of the right triangle by 15 m.
Must be something to do with tangent, don't you think?
2006-12-03 19:45:20 · answer #3 · answered by arbiter007 6 · 0⤊ 0⤋
2,146 feet
2006-12-03 19:46:06 · answer #4 · answered by rep the bay 2 · 0⤊ 0⤋