<span>The line of symmetry of the triangle bisects the right angle and the diagonal of the square.
The line is 1/2 the length of the square's diagonal :
(1/2)(10√2) = 5√2.
</span>Let CG be a distance x from the vertex of the right angle in the triangle.
Remaining distance = 5√2 - x.
<span>
(1)(x) = (2)(5√2 - x)</span>
x = 10√2 - 2x
<span>3x = 10√2 </span>
<span>x = (10/3)√2.
</span>
Using Pythagorean theorem,
x^2 + y^2 = c^2
<span>c = (10/3)√2,
and x = y,
so 2x^2 = 200/9
x = √(100/9) = 10/3 = y.
</span>
<span>x = y = 3.333</span>
0.92085175 radians
Let's first calculate the length of the diagonal of the base. Using the Pythagorean theorem:
b = sqrt(9^2 + 7^2) = sqrt(81 + 49) = sqrt(130) = 11.40175425
Now the length of the diagonal to the box. Once again, using the Pythagorean theorem:
d = sqrt(15^2 + 11.40175425^2) = sqrt(225 + 130) = sqrt(335) = 18.84144368
We now have a right triangle where we know the lengths of all three sides. The lengths are:
a = 15
b = sqrt(130) ≠11.40175425
c = sqrt(335) ≠18.84144368
we want the angle opposite to side a. So
tan(A) = 15/11.40175425 = 1.315587029
A = atan(1.315587029)
A = 0.92085175 radians
8=3(3x+8)-x
8=9x+24-x
-16=8x
x= -2
The right answer is D 1/3x4/3
