Hello, symmetry!

At Mogul’s Ski Resort, the beginner’s slope is inclined at an angle of 12.3°

while the advanced slope is inclined at an angle of 26.4°.

If Rudy skis 1,000 meters down the advanced slope

while Valerie skis the same distance on the beginner’s slope,

how much longer was the horizontal distance that Valerie covered?

(1) 81.3 m . . (2) 231.6 m . . (3) 895.7 m . . (4) 977.0 m Code:

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* :
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* 1000 * :
* : * :
1000 * : * :
* : * :
* 12.3° : * 26.4° :
* - - - - - - - - - * * - - - - - - - *
V R

The first triangle represents the beginner's slope.

. . Let $\displaystyle V$ = Valerie's horizontal distance.

We see that: .$\displaystyle \cos12.3^o \;=\;\frac{V}{1000}\quad\Rightarrow\quad V \;=\;1000\cdot\cos12.3^o \;=\;977.0455744$

The second triangle represents the advanced slope.

. . Let $\displaystyle R$ = Rudy's horizontal distance.

We see that: .$\displaystyle \cos26.4^o \;=\;\frac{R}{1000}\quad\Rightarrow\quad R\;=\;1000\cdot\cos26.4^o \;=\;895.7117602$

The difference is: .$\displaystyle 977.0455744 - 895.7117602 \;\approx\;81.3\text{ m}$ . . . answer (1)