deductive geomertry

Question

 a water slide is 4.2m high and has a support 2.4m tall. if a student reaches this support when she is 3.1m down the slide, how long is the slide ?a water slide 

Answer 1

 Wow.  That was a nice problem.  First thing I did was get more information on the smaller triangle with hypoteneuse of 3.1, opposite of 4.2-2.4 = 1.8 and adjacent of sqrt(3.1^2 -1.8^2) using pythagorean theorem.  To find angle X, Cos(X) = adj/opp.  Inverse Cosine of X = 35.5 degrees.  TAN (X) = opp/adj = 0.7132 = 4.2/adjacent, giving adjacent 5.889 on larger triangle.  Then hypoteneuse * COS (X) = 5.889.  Solving for hypoteneuse gives us 5.889/COS(X) = 7.2 meter. 

 

I wish I could have included my sketches, but that option is not available.   
 

Answer 2

First, Geometry, not geomertry.

 

If the side view is essentially a right triangle with vertical leg = 4.2 m and the slide is its hypotenuse, and if the support creates a second right triangle similar to the first one, then let's say that the small hypotenuse is x; then by corresponding ratios, we have x/2.4 = (x+3.1)/4.2 (small hypotenuse is to support height as overall hypotenuse is to 4.2 larger right triangle's height).

 

This leads to x = 4.1333 m so the overall slide length is 7.2333 m