The polygons are similar. Find the value of x.

Mathematics

2 answers:

dmitriy555 [2]2 years ago

7 0

Answer:

x = 30

Step-by-step explanation:

12 : 20 = 18 : x

⇒ 12/20 = 18/x

⇒ 12x = 18 · 20

⇒ 12x = 360

⇒ x = 360 ÷ 12

⇒ x = 30

Ivahew [28]2 years ago

7 0

$\\ \rm\Rrightarrow \dfrac{21}{x}=\dfrac{14}{20}$

$\\ \rm\Rrightarrow \dfrac{21}{x}=\dfrac{7}{10}$

$\\ \rm\Rrightarrow 7x=210$

$\\ \rm\Rrightarrow x=30$

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Xelga [282]

Given a right triangle with hypothenus of measure 34, the side opposite the angle θ of measure 30, and the side adjacent the angle theta of measure 16.

$\sin\theta= \frac{opposite}{hypothenuse} = \frac{30}{34} = \frac{15}{17} \\ \\ \Rightarrow \theta=\sin^{-1}\left( \frac{15}{17} \right) \\ \\ \\ \cos\theta= \frac{adjacent}{hypothenuse} = \frac{16}{34} = \frac{8}{17} \\ \\ \Rightarrow \theta=\cos^{-1}\left( \frac{8}{17} \right) \\ \\ \\ \tan\theta= \frac{opposite}{adjacent} = \frac{30}{16} = \frac{15}{8} \\ \\ \Rightarrow \theta=\cos^{-1}\left( \frac{15}{8} \right)$