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Two right triangles share a side as follows.  What is the distance from C to line AD?

 

 Feb 15, 2022
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Draw CX from point C perpendicular to line AD, with X on AD.

The length of CX is the distance from C to line AD.

 

Triangle(CXA) will be a right triangle with CA the hypotenuse.

 

Since triangle(DAB) is an isosceles right triangle with the right angle at B, 

angle(DAB) = 45o.

 

This makes angle(CAD) = 45o.

 

For triangle(CAX), sin( angle(CAX) ) = CX / CA.

--->                                      sin(45o)  =  CX / 10

 

Finish this equation to find the length of CX, the distance from C to line AD.

 Feb 15, 2022

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