3 years ago

Heather's class took a field trip to the science museum. They left school at 7:30 A.M. It took

Mathematics

1 answer:

vodka [1.7K]3 years ago

5 0

Answer:

10:30 A.M

Step-by-step explanation:

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

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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 :

$\cos(θ) = \frac{adj.}{hypo.}$

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

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

$CD \cos(36.9) = 5$

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

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

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