Answers:
- segment MU = 3*sqrt(47) = 20.56696
- Angle E = 47.26789 degrees
- Angle U = 42.73211 degrees
The decimal values are approximate.
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Work Shown:
Let x be the length of segment MU
We'll use the pythagorean theorem to find x. This works because we have a right triangle.
a^2 + b^2 = c^2
19^2 + x^2 = 28^2
x^2 = 28^2 - 19^2
x^2 = 784 - 361
x^2 = 423
x = sqrt(423)
x = sqrt(9*47)
x = 3*sqrt(47)
Segment MU is exactly 3*sqrt(47) units long. That approximates to 20.56696
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We'll use the cosine ratio to find angle E
cos(angle) = adjacent/hypotenuse
cos(E) = EM/UE
cos(E) = 19/28
E = arccos(19/28)
E = 47.2678899573979
E = 47.26789
Angle E is roughly 47.26789 degrees
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Since angles U and E are complementary, we can then say,
U+E = 90
U = 90 - E
U = 90 - 47.26789
U = 42.73211
Angle U is roughly 42.73211 degrees.