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Andrew [12]
3 years ago
13

Is a circles area proportional to its radius? Is a circles circumference proportional to its diameter?

Mathematics
1 answer:
tia_tia [17]3 years ago
6 0
In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
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In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°. Find all possible values of ∠X, to the nearest degree.
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Given:

In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°.

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The all possible values of ∠X, to the nearest degree.

Solution:

Law of Sines:

\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}

For ΔWXY,

\dfrac{w}{\sin W}=\dfrac{x}{\sin X}=\dfrac{y}{\sin Y}

Now,

\dfrac{w}{\sin W}=\dfrac{x}{\sin X}

\dfrac{900}{\sin (157^\circ)}=\dfrac{680}{\sin X}

900\sin X=680\sin (157^\circ)

\sin X=\dfrac{680}{900}\sin (157^\circ)

\sin X=0.295219

X=\sin^{-1}(0.295219)

X=17.17067

X\approx 17

Therefore, the value of ∠X is 17 degrees.

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