+1859 help im bad at geo
In the diagram below, $ABCDEFGH$ is a cube. Find $\sin \angle GAC$. Find $\sin \angle HAC$.
+129771 GAC forms a right triangle with the right angle at G
The other two sides are equal sides of the cube such that GC = GA
So this forms an isosceles right riangle....so angle GAC = 45°....and the sin 45° = sqrt (2) / 2
HAC is a little more difficult to see.....let's call the side of the cube = 1 = HA
AC = the diagonal across the face of the cube = sqrt (2)
And HC is the major diagonal of the cube = sqrt (3)
Then HAC must form a right triangle because
HA^2 + AC^2 = HC^2
1^2 + (sqrt 2)^2 = (sqrt 3)^2
1 + 2 = 3
And angle HAC is opposite the hypotenuse in this triangle so its measure = 90°....and sin HAC = sin 90° = 1
