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3 years ago

HELP DUE IN 10 MINS! Find the scale factor. Solve for x. Scale Factor=?? x=??

Mathematics

1 answer:

stepladder [879]3 years ago

4 0

Answer:

Scale factor = 1/2 and x = 18

Step-by-step explanation:

Given:

ΔABC ~ ΔDEF
AB = 36. BC = 30
DE = x, EF = 15
m∠B = m∠E = 72°

Corresponding sides are:

AB and DE
BC and EF

Corresponding sides have same ratio:

AB/DE = BC/EF
36/x = 30/15
x = 36/2
x = 18

The scale factor is:

DE/AB = 36/18 = 1/2

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3 years ago

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Answer:

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Step-by-step explanation:

Trigonometric Identities

$\sin (A \pm B)=\sin A \cos B \pm \cos A \sin B$

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Therefore, using the trig identities and ratios:

$\begin{aligned}\sin (\angle BAC + 30^{\circ}) & = \sin (\angle BAC) \cos (30^{\circ})+\cos (\angle BAC) \sin (30^{\circ})\\\\& = \dfrac{16}{20} \cdot \dfrac{\sqrt{3}}{2} + \dfrac{12}{20} \cdot \dfrac{1}{2}\\\\& = \dfrac{16}{40}\sqrt{3}+\dfrac{12}{40}\\\\& = \dfrac{2}{5}\sqrt{3}+\dfrac{3}{10}\end{aligned}$

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