XYZ is an isosceles triangle with |XY|=|XZ|=6cm and angle XYZ=120°. Calculate the length of line YZ.
using sin rule
x/sin120°=6/sin30°
.
sin120°= √3/2 and sin30°= 1/2
x/√3/2 = 6/1/2
2x/√3 = 12
x= 12*√3/2
x= 6√3cm.. (answer)
120 + 2 x = 180
x = 30 degrees for the other two angles
cos 30 = (YZ/2)/6
cos 30 = yz/12
yz = 12 cos 30
This is prefect for the law of cosines, have you had that?
Ok, if you have not, thenisosceles means angle x and z are 60 degrees. So bisect angle xyz, it forms two triangles. Note the bisected angle forms each 60 degrees, so not each of the two new triangles have two angles of 60...oh oh, that means the third angle is 60 degrees, and they are equilateral triangles, all angles and sides equal. Now you can figure then the XZ is now 12 (two sixes on each triangle.)
I need the angle to be drawn
Cos30=0.8660
0.8660÷12
=0.9996