1 Answer

Conall · Answer 1 · 2021-07-09T13:04:29+0000

Answer:

The answet is C.

Explanation:

First, you have to find the angle of ACB using Sine Rule, sinθ = opposite/hypotenuse :

$\sin(θ ) = (oppo.)/(hypo.)$

$let \: oppo. = 4 \\ let \: hypo. = 5$

$\sin(θ) = (4)/(5)$

$θ = {\sin( (4)/(5) ) }^( - 1)$

$θ = 53.1 \: (1d.p)$

Given that line AB is parallel to line CD so ∠C = 90°. Next, you have to find the angle of ACD :

ACD = 90 - 53.1 = 36.9

Lastly, you can find the length of CD using Cosine rule, cosθ = adjacent/hypotenuse :

$\cos(θ) = (adj.)/(hypo.)$

$let \: θ = 36.9 \\ let \: adj. = 5 \\ let \: hypo. = CD$

$\cos(36.9 ) = (5)/(CD)$

$CD \cos(36.9) = 5$

$CD = (5)/( \cos(36.9) )$

$CD = 6.25 units\: (3s.f)$

Please log in or register to add a comment.