Angle of depression from top of a building that is 252 meters tall, to a point on the ground is 32.5 degrees. To the nearest tength, how far is the base of the building to that point on the ground?
B
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A C
angle C is 32.5, AB is 252 meters... I gotta find AC..
tan32.5 = 252 / x (AC)
Am I on the right track? Do I use inverse or tan?.. what do I do next?
2007-05-21 13:38:43 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Nevermind! I'm sorry. I was stumbled as to why my answer didn't match the one in the book. My calculator was set to radians, not degrees!
2007-05-21 15:59:53 · update #1
You're on the right track.
In your diagram:
tan(angle C) = opposite/adjacent = AB/AC
What you do next is place the known values in the equation. (Angle C is the same as the angle of depression from the top of the building, an alernate interior angle using the ground and an imaginary line parallel to the ground through point B.)
tan(32.5) = 252 / AC
You can rearrange it to get the unknown by itself:
AC = 252 / tan(32.5)
... then all you need to do is get tan(32.5) from your calculator and divide.
2007-05-21 13:42:25 · answer #1 · answered by McFate 7 · 0⤊ 0⤋
If angle c is 32.5, then you know that angle B is 67.5. From there, you can use the law of sines: sinA/a=sinB/b=sinC/c, or you can use tan(67.5)=a/c, but since you don't know c, I suggest using the law of sines.
sin(67.5)/b=sin(32.5)/252
makes it 252*sin(67.5)=b*sin(32.5)
Divide by sin(32.5): b=252sin(67.5)/sin(32.5)
b=433.3m
-Corkeoes
2007-05-21 20:48:25 · answer #2 · answered by corkeoes 1 · 0⤊ 0⤋
tan32.5 = AC/252
AC = 160.5 (to 1 decimal place)
2007-05-21 20:52:00 · answer #3 · answered by anonymous 2 · 0⤊ 0⤋
x = (252meter)/(tan32.5º).
2007-05-21 20:43:14 · answer #4 · answered by Mark 6 · 0⤊ 0⤋