Question #3c052

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Answer 1 · 2017-11-23T19:36:58

$theta = Pi/6$

$x = 4.5sqrt2$

ABC is a right angle triangle with 2 sides given
Hypotenuse = 8
Opposite = 4

$Sin theta = 4/8$

$theta = Pi/6$

The internal angles of a triangle add up to $pi$
$/_ACB = pi - pi/6 - pi/2$
therefore $/_ACB = pi/3$

Opposite angles mean that $/_DCF = pi/3$
$/_DCF = /_DCE +/_FCE$

Substitute in what we know
$Pi/3 = Pi/12 + /_FCE$

$/_FCE = Pi/4$

$Cos x = (adjacent)/(hypoten use)$

therefore
$cos(pi/4) = 4.5/x$

rearrange
$x = 4.5/cos(pi/4) = 4.5/(1/sqrt2) = 4.5sqrt2$