How can I find the height of a scalene triangle given its side angles, 6, 8, and 10?
+130478 How can I find the height of a scalene triangle given its side angles, 6, 8, and 10?
You don't have a scalene triangle, you have a right triangle. If its hypoteneuse (the side with the measure of 10) isn't the base, then it's height is either 6 or 8, depending on the orientation of the triangle.
If the hypoteneuse is the base, it's a little more difficult. Let us orient the triangle so that the hypoteneuse is the base and the side with the length of 8 is on the "left" side of the triangle. Using the law of sines, we can find the sine of the angle that lies between the side with length 8 and the hypoteneuse. We can just label this angle as "A."
sin 90 / 10 = sin A / 6 which gives us
sin A = 6 /10= .6
Now, draw a perpendicular from the base to the apex ....this is the height (h)
And using the law of sines again (and realizing that the perpendicular forms a right angle), we have
h / sin A = 8 / sin 90
h / .6 = 8
h = 8(.6) = 4.8
That one was a little tougher !!! 
+118706 How can I find the height of a scalene triangle given its side angles, 6, 8, and 10?
Chris was right when he said that this is a right angled triangle but it is ALSO A SCALENE TRIANGLE.
So you can use 6 as the base and 8 as the height
or
you can use 8 as the base and 6 as the height.
or
you can use 10 as the base and do all that working that Chris did to get the height.
