Question

Question #3c052

Answer 1

`theta = Pi/6`

`x = 4.5sqrt2`

Explanation:

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`