Math CentralQuandaries & Queries


Question from Jaylynn, a student:

Hi, I've been trying to figure out how long my ramp would have to be in order to reach a height of 3.5 feet at a 30 degree angle for a sugar glider enclosure?

Hi Jaylynn,

Suppose the length of the ramp is $r$ feet then I get the diagram


The ramp forms a right triangle and the sine of the $30^o$ angle is thus $\frac{3.5}{r}.$ But the sine of a $30^o$ angle is $\frac12$ and thus

\[\frac{3.5}{r} = \frac12 .\]

Threrfore $r = 2 \times 3.5 = 7$ feet.


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