The law of sines and cosines


label Calculus
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A lamp post tilts toward the sun at a 2 degree angle from the vertical and casts a 25 foot shadow. The angle from the tip of the shadow to the top of the lamp post is 45 degrees. Find the length of the lamp post.

Dec 11th, 2014

The law of sines says that for any triangle the sine of any angle is proportional to the length of the opposite side.

In your problem the height of the lamppost is opposite the 45 deg angle and the known length of the shadow is opposite an angle of43deg.

Therefore sin43/25 = sin45/x

solve for x, x=(sin45/sin43)*25 = 25.92 feet... this is the answer :)

Please best my answer if helpful :)

Dec 11th, 2014

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Dec 11th, 2014
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