Horizontal Distance

At Mogul’s Ski Resort, the beginner’s slope is inclined at an angle of 12.3o while the advanced slope is inclined at an angle of 26.4o 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 (3) 895.7 m
(2) 231.6 m (4) 977.0 m

Hello, symmetry!

Quote:

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:

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

The first triangle represents the beginner's slope.
. . Let $V$ = Valerie's horizontal distance.
We see that: . $\cos12.3^o \;=\;\frac{V}{1000}\quad\Rightarrow\quad V \;=\;1000\cdot\cos12.3^o \;=\;977.0455744$

The second triangle represents the advanced slope.
. . Let $R$ = Rudy's horizontal distance.
We see that: . $\cos26.4^o \;=\;\frac{R}{1000}\quad\Rightarrow\quad R\;=\;1000\cdot\cos26.4^o \;=\;895.7117602$

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

ok

I had no idea trigonometry was needed to solve this question.

Thanks!