The Uneven Parking Lot

Geometry Level 1

You have parked your car on a parking lot with a consistent 1 degree tilt downward from east to west. Your eyes are precisely 6 feet above the ground while standing on the low west side. How long must the distance of the parking lot be if you are at eye-level with the pavement of the east side of the parking lot?

140.3 ft. 11.1 ft. 343.8 ft. 7.1 ft.

Nicholas Walters by Nicholas Walters , 21, USA

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2 solutions

Marta Reece
Jul 17, 2017

The distance is to be measured along the slanting parking lot, so the setup is

sin ⁡ 1 ∘ = 6 x \sin 1^\circ=\dfrac6x

x = 6 sin ⁡ 1 ∘ ≈ 343.8 x=\dfrac 6{\sin 1^\circ}\approx\boxed{343.8}

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From the figure,

sin ⁡ 1 ∘ = 6 l e n g t h o f p a r k i n g l o t \large \sin~1^\circ=\dfrac{6}{length~of~parking~lot}

l e n g t h o f p a r k i n g l o t = 6 sin ⁡ 1 ∘ ≈ \large length~of~parking~lot=\dfrac{6}{\sin~1^\circ} \approx 343.8 \color{#D61F06}\boxed{\large 343.8}

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