Please show work! Thank you!

Step-by-step explanation:

21)

The sine rule is expressed as

a/SinA = b/SinB = c/SinC

Where a, b and c are the length of each side of the triangle and angle A, Angle B and angle C are the corresponding angles of the triangle. Therefore,

12/Sin 64 = x/Sin 12

Cross multiplying, it becomes

xSin 64 = 12Sin12

xSin 64 = 12 × 0.209

0.8988x = 2.508

x = 2.508/0.8988

x = 2.79

The sum of the angles in a triangle is 180 degrees. Therefore, the unknown angle in triangle is

180 - (64 + 12) = 104 degrees. Therefore,

y/Sin104 = 12/Sin64

ySin64 = 12Sin104

0.8988y = 12 × 0.9703 = 11.6436

y = 11.6436/0.8988

y = 12.95

22) we would apply the law of Cosines which is expressed as

a² = b² + c² - 2bcCosA

Therefore,

28² = 20² + 24² - 2 × 20 × 24Cosx

784 = 400 + 576 - 960Cosx

784 = 976 - 960Cosx

960Cosx = 976 - 784 = 192

Cosx = 192/960 = 0.2

x = Cos^(-1)0.2

x = 78.5°

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option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have