Trigonometry problem about height of a pole?

Question

A pole tilts toward the sun and it has an angle of 8 degrees from the vertical and it casts a 22 foot shadow. THe angle of elevation from the tip of the shadow to the top of the pole is 43 degrees. How long is the pole?

Answer 1

The pole leans 8° from vertical and tilts toward the sun. So the angle on the side of the shadow is

90 + 8 = 98°

The angle of elevation is 43°.

The third angle at the top of the pole is

180 - 98 - 43 = 39°

Now apply the law of sines. Let the length of the pole be p.

p/sin43° = 22/sin39°
p = 22(sin43°/sin39°) ≈ 23.84 ft
________

The gentleman above has the right idea, but he has the pole tilting in the wrong direction.

Answer 2

8 degrees from the vertical. That means 82 degrees from the horizon.

let h be the length of the pole.

draw a diagram.
The measure of the third angle is 180 - (82 + 43) = 55

Use Sine law
h/sin(43) = 22/sin(55)
h = sin(43)22 / sin(55)
h =~ 18.3 ft <== answer

edit: oh yeah! i forgot about that detail.

Answer 3

with this one, you may imagine a triangle. Given is the bottom (B) it really is 10 ft. and the perspective that the cord makes with the bottom is 75degrees. what's lacking is the right of the pole (P) and the dimensions of the cord (W). because the pole is declared to be vertical, then this skill the pole and the bottom makes an perspective of 90degrees. with this shall we employ sin, cos, and tangent. fixing for P: tan seventy 5 = P/B P = Btan75 P = 10tan75 P = 37.32 ft. fixing for W: cos seventy 5 = B/W W = B/(cos75) W = 10/(cos75) W = 38.6 ft.