Posted by **AEF** on Tuesday, June 5, 2012 at 11:03am.

A straight road makes an angle, A of 12 degrees. When the angle of elevation, B, of the sun is 55 degrees, a vertical pole beside the road casts a shadow 7 feet long parallel to the road. Approximate the length of the pole. Round to tow decimal places.

- calculus -
**Steve**, Tuesday, June 5, 2012 at 11:57am
draw a diagram.

P = end of shadow on road

T = top of pole

Q = foot of pole

Z = intersection of horizontal line from Q and pole extended vertically.

Let d = PT: the distance from the tip of the shadow to the top of the pole

Let x = PZ

Let y = ZQ

Let h = QT, the height of the pole

We know:

∠ZPT = 55°

∠ZPQ = 12°

so, ∠QPT = 43°

PQ = 7

x = 7cos12° = 6.847

y = 7sin12° = 1.455

d = x/cos55° = 7cos12°/cos55° = 11.937

now, we can do this two ways

(1) Pythagorean Theorem

x^2 + (y+h)^2 = d^2

h = 8.323

(2) Law of Cosines

h^2 = d^2 + 7^2 - 2*7*d*cos43°

h = 8.323

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