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Geometry Level 2

A person stands 40 m from a flag pole. With a protractor at eye level, he finds the angle at the top of the flag pole with the horizontal is 25.0 degrees. How high is the flag pole? The distance from his feet to his eyes is 1.8 m.


The answer is 20.4.

Fares Salem by Fares Salem , 22, Egypt

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2 solutions

tan ⁡ 25 = x 40 \tan~25=\dfrac{x}{40} ⟹ \implies x = 40 tan ⁡ 25 x=40 \tan~25

h = 1.8 + x = 1.8 + 40 tan ⁡ 25 ≈ h=1.8+x=1.8+40 \tan~25\approx 20.452 m 20.452~m

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John Taylor
Mar 23, 2015

If the distance to the flagpole is 40 meters, and the angle formed by the imaginary line from the person's eyes to the flagpole is 25 degrees, an inverse tangent function can solve for the height of the pole from eye level, which is 18.6 meters. Adding the 1.8 meters that represented the distance from eye level to the ground gives the height of the flagpole as 20.4 meters.

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