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# person test

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When the sun shines at a 60º angle to the ground, Noemi’s shadow is 39 in. long. To the nearest inch, how tall is Noemi?

Apr 7, 2021

#1
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since the angle is 60, we know it's a 30 60 90 triangle.

this means her height is 39 ÷ √3 = 13√3 ≈ 22.52 inches.

Apr 7, 2021
#2
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It is a 30 60 90 triangle as described, but the short side of the triangle opposite the 30° angle is the length of the shadow, or 39".

Naomi is the long side of the triangle opposite the 60° angle.  Therefore her height as a function of the length of the shadow is:

$$height = shadow \sqrt 3$$

$$height = 39 \sqrt3 \approx 67.5$$

Rounding the above to the nearest inch makes Naomi 68 inches tall, or 5 ft. 8".

Apr 7, 2021