Trig help word problem?

Question

A ten meter pole casts a 17 meter shadow directly down a slope when the angle of the sun is 42 degrees. Find the angle of the elevation of the ground.


This one needs to be drawn out. But, I am so confused. I know that you need to make a right triangle. That means that the right angle is below ground. The 42 degrees is then the angle from underground to the top of the telephone pole. I need to know the angle from the underground portion of the corner to the bottom of the pole. Help please.

Answer 1

Let
θ = desired angle
α = 42° - θ = the angle above ground to the top of the flag pole
θ = 42° - α

Use triangles and the Law of Sines. Look at the non-right triangle formed by the base of the flag pole, the top of the flag pole, and the tip of the shadow of the flag pole.

We already know two of the sides. The vertical side is 10m. The shadow is another side that is 17m.

If angle of the sun is 42° above a level horizon, then the angle at the top of the flag pole is δ = 90 - 42 = 48°. Now we can measure α.

17/sin(48°) = 10/sin α
sin α = [10 sin(48°)]/17
α = arcsin{[10 sin(48°)]/17} ≈ 25.9°

θ = 42° - α ≈ 42° - 25.9° = 16.1°

Answer 2

So you have a pole on a hill that's casting a shadow downward on the hill. Draw a tall but somewhat skinny right triangle where the bottom leg is horizontal, the other leg is to the left and veritcal (so it's just like an "L" with the two ends connected). Label the top point D, the right-angle point B, and the other bottom point C. Now pick a point around the middle of BD and call it A. Draw a line between A and C. You now have a picture of what's going on, where AD is the pole and AC is the shadow, which is also the surface of the hill. Triangle ABC is underground. We want to find angle ACB. Call this "x".

We know angle BCD is 42. Since DBC is a right triangle, then angle BDC must be 90-42=48. Also, angle ACD must be 42-x.

Look at triangle DAC. Using the law of sines, we have:

sin(48)/17 = sin(42-x)/10.

So solve this for x:

sin(42-x) = 10sin(48)/17
42 - x = sin^-1 (10sin(48)/17)
42 = sin^-1 (10sin(48)/17) + x
x = 42 - sin^-1 (10sin(48)/17)
This is about 16.078 degrees

Answer 3

I got the angle of elevation as 16.08deg. I don't know how to draw the skecth here though. If you can get the skecth right, the solution is easier to find. Contact me if u want me to e-mail the sketch