Asked by Keserie
A straight road slopes upward 14 degrees from the horizontal. A vertical telephone pole beside the road casts a shadow of 60 feet down the road. if the angle of elevation of the sun is 55 degrees, what is the height of the telephone pole?
Answers
Answered by
Steve
draw a diagram.
Label these points:
T = top of pole
B = base of pole on road
S = tip of shadow on road
Draw a horizontal line from S to where it intersects the extension of TB below the road. Call that point C.
Now, we want the height h = BT
Let
x = SC
y = CB
Now, we have
y/60 = sin 14°
x/60 = cos 14°
(h+y)/x = tan 55°
Combine all that to get
(h+60sin14°)cot55° = 60cos14°
I get h = 68.63 feet
Label these points:
T = top of pole
B = base of pole on road
S = tip of shadow on road
Draw a horizontal line from S to where it intersects the extension of TB below the road. Call that point C.
Now, we want the height h = BT
Let
x = SC
y = CB
Now, we have
y/60 = sin 14°
x/60 = cos 14°
(h+y)/x = tan 55°
Combine all that to get
(h+60sin14°)cot55° = 60cos14°
I get h = 68.63 feet
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