Slide Height

Geometry Level pending

A slide is made by joining a 6 unit ladder to an 8 unit chute at right angles. Find the vertical height, in units, of the slide.


The answer is 4.8.

Tan Chee Sen by Tan Chee Sen , 25, Malaysia

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3 solutions

Ashish Manchanda
Jul 16, 2014

1/2×8×6=1/2×10×h, h=4.8

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Consider the diagram.

tan ⁡ a = 6 8 = 3 4 \tan a=\dfrac{6}{8}=\dfrac{3}{4} ⟹ \implies a = tan ⁡ − 1 3 4 a=\tan^{-1} \dfrac{3}{4}

sin ⁡ a = h 8 \sin a=\dfrac{h}{8} ⟹ \implies h = 8 sin ⁡ a = 8 sin ⁡ [ t a n − 1 3 4 ] = 4.8 f e e t h=8 \sin a=8 \sin \left[tan^{-1} \dfrac{3}{4} \right] = \boxed{4.8~feet}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Consider the diagram on my left.

By similar triangles, we have

8 10 = h 6 \dfrac{8}{10}=\dfrac{h}{6}

h = 8 ( 6 ) 10 = 48 10 = h=\dfrac{8(6)}{10}=\dfrac{48}{10}= 4.8 \boxed{4.8}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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