Question 893046
Drawing this triangle will help to analyze it.
Base is 26 cm.
Put the 10 cm side at the left, and put the 24 cm side at the right;
make the 10 and 24 cm sides meet at a vertex above the base.
Label the angle where the 10 and 26 cm lengths meet as alpha; show the height y as the perpendicular distance from the top vertex to the base.  Note that y meets the base, the 26 cm length base, at a right angle.


Check to see if the given triangle itself is a right triangle:
{{{10^2+24^2=26^2}}}
{{{100+576=676}}}
YES.  The vertex above the base IS ALSO a right angle, so this given triangle is also a right triangle.


LAW of SINES TO FIND alpha:
{{{sin(alpha)/24=sin(90)/26}}}
{{{sin(alpha)=(24/26)sin(90)}}}
{{{sin(alpha)=(12/13)*1}}}
{{{highlight_green(alpha=arcsin(12/13))}}} ------you can compute the decimal approximation whenever you want.


Give attention now to the right trianlge bound by the 10 cm side, the distance y, and the base.  


FINDING y:
{{{sin(alpha)=y/10}}}, basic trigonometry
{{{y=10*sin(alpha)}}}, and you already found sin(alpha);
{{{highlight(y=10*(12/13))}}}----ANSWER