Aflagpole is perpendicular to the horizontal but iis on a slope that rises 10 degrees from the horizontal. the pole casts a 43-foot shadow down the slope and angle of elevation of the sun measured from the slope is 36 degrees. how tall is the pole?

36 ft. The flagpole and the shadow create a triangle with the angle at the base of the flagpole being 100 degrees. The angle at the end of the shadow being 36 degrees and the angle at the top of the flagpole is 180-100-36 = 44 degrees. We know the length of the shadow is 43 feet, and using the law of sines, we get sin(44)/43 = sin(36)/X where X is the height of the flagpole. So let's solve for X sin(44)/43 = sin(36)/X Xsin(44)/43 = sin(36) Xsin(44) = 43sin(36) X = 43sin(36)/sin(44) X = 43 * 0.587785252/0.69465837 X = 36.38445446 Rounding to 2 significant figures, gives us a height of 36 ft.

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