A central angle measuring 120° intercepts an arc in a circle whose radius is 3.

Mathematics

1 answer:

Kisachek [45]3 years ago

5 0

Answer:

6.28

Step-by-step explanation:

The length of arc which subtends an angle $\alpha$ at the center of a circle is given by $\alpha r$ where r is the radius of circle.

______________________________

given

the central angle of arc is 120°

$\pi = 180\\120 = (\pi /180)* 120\\120 = 2/3\pi$

we will use value of $\pi$ as 3.14

r = 3

Length of this arc is

$2/3( \pi *3) = 2\pi \\=2*3.14 = 6.28$

The length of the arc to the nearest hundredth of unit is 6.28

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2 years ago

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Naddika [18.5K]

Answer:

cos(z) = .3846153846 and angle z = 67.38°

Step-by-step explanation:

Side UV is corresponding to side YX. Side VW is corresponding to side YZ. Side UW is corresponding to side XZ.

Starting with the first corresponding pair, we are told that side UV is 36, and that side YX is 3/5 of that. So side YX is

$\frac{3}{5}*36=21.6$

We are next told that side VW is 39, so side YZ is

$\frac{3}{5}*39=23.4$

In order to find the cos of angle z, we need the adjacent side, which is side XZ. Side XZ is 3/5 of side UW. Right now we don't know the length of side UW, so we find it using Pythagorean's Theorem:

$39^2-36^2=UW^2$ and