Thread: law of sines

i having a hard time drawing the picture for this word problem and also knowing what angles i should use for the law of sines. i hope someone can help me!!

a flagpole at right angle to the horizontal is located on a slope that makes an angle of 12 degrees with the horizontal. the pole's shadow is 16 meters long and points directly up the slope. the angle of elevation from the tip of the shadow to the sun is 20 degrees. what is the height of the pole? (hint: draw a triangle and apply the law of sines. note that the shadow points up the slope starting from the bottom of the flag pole. the angle of elevation is the angle made with the horizontal not with the ground)

Originally Posted by elizabeth292

i having a hard time drawing the picture for this word problem and also knowing what angles i should use for the law of sines. i hope someone can help me!!

a flagpole at right angle to the horizontal is located on a slope that makes an angle of 12 degrees with the horizontal. the pole's shadow is 16 meters long and points directly up the slope. the angle of elevation from the tip of the shadow to the sun is 20 degrees. what is the height of the pole? (hint: draw a triangle and apply the law of sines. note that the shadow points up the slope starting from the bottom of the flag pole. the angle of elevation is the angle made with the horizontal not with the ground)

I hope this helps.

RonL

" a flagpole at right angle to the horizontal is located on a slope that makes an angle of 12 degrees with the horizontal. the pole's shadow is 16 meters long and points directly up the slope. the angle of elevation from the tip of the shadow to the sun is 20 degrees. what is the height of the pole? "

If you cannot draw the figure, then just imagine it as an obtuse triangle, with these:
>>>one side is vertical, representing the heigth of the pole. Call it x.
>>>one side is sloping at 12deg from horizontal, representing the length of the shadow of the pole. It is 16m long.
>>>the third side is sloping at 20deg from the horizontal, representing a ray of the sun. Its length is unknown. Call it z.

That means:
1) the angle included by the two sloping sides is 20 -12 = 8deg.
2) the angle included by the x and z sides is 90 -20 = 70deg.

Then, by Law of Sines,
x / sin(8deg) = 16 / sin(70deg)

Multiply both sides by sin(8deg),
x = [16 / sin(70deg)]*sin(8deg)
x = 2.37 m. -----------height of pole, answer.

----------------
Ummm, I missed the "...up the slope..."
Corrections then:

That means:
1) the angle included by the two sloping sides is 20 +12 = 32deg.
2) the angle included by the x and z sides is 90 -20 = 70deg.

Then, by Law of Sines,
x / sin(32deg) = 16 / sin(70deg)

Multiply both sides by sin(32deg),
x = [16 / sin(70deg)]*sin(32deg)
x = 9.02, or 9 m. -----------height of pole, answer.

wow! you make it look so easy. that was so helpful--thanks a lot!