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

Guest Feb 15, 2022

#1**+1 **

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) = 45^{o}.

This makes angle(CAD) = 45^{o}.

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

---> sin(45^{o}) = CX / 10

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

geno3141 Feb 15, 2022