Question

What is the length, in units, of segment CD?

Answer 1

Answer:

The answet is C.

Step-by-step explanation:

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

$\sin(θ ) = \frac{oppo.}{hypo.}$

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

$\sin(θ) = \frac{4}{5}$

$θ = {\sin( \frac{4}{5} ) }^{ - 1}$

$θ = 53.1 \: (1d.p)$

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 :

$\cos(θ) = \frac{adj.}{hypo.}$

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

$\cos(36.9 ) = \frac{5}{CD}$

$CD \cos(36.9) = 5$

$CD = \frac{5}{ \cos(36.9) }$

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