The distance: use absolute value
Between x and 8: x-8
The distance between x and 8: | x-8 |
“is no more than” means it can be that or be less than that, so use ≤
The distance between x and 8 is no more than 4
| x-8 | ≤ 4
Let
x = 3a (first angle)
y = 3a (second angle)
z = 6a (third angle)
The total angle of a triangle is ALWAYS 180.
3a + 3a + 6a = 180
12a = 180
a = 15
Therefore, x = 45, y = 45, z = 90
The identity in question is
cos(a - b) = cos(a) cos(b) + sin(a) sin(b)
so that
cos(a - b) = 12/37 cos(a) + 3/5 sin(b)
Since both a and b lie in the first quadrant, both cos(a) and sin(b) will be positive. Then it follows from the Pythagorean identity,
cos²(x) + sin²(x) = 1,
that
cos(a) = √(1 - sin²(a)) = 4/5
and
sin(b) = √(1 - cos²(b)) = 35/37
So,
cos(a - b) = 12/37 • 4/5 + 3/5 • 35/37 = 153/185
