Question

Use the law of sines to find the value of w.

Triangle U V W is shown. Angle V W U is 39 degrees and angle W U V is 31 degrees. The length of V W is 3.3 centimeters and the length of U V is w.

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

What is the best approximation of the value of w?

1.4 cm
4.0 cm
6.0 cm
7.3 cm

Answer 1

it is the answer b 4.0 cm

Step-by-step explanation:

Answer 2

Option B: 4.0 cm is the value of w

Step-by-step explanation:

It is given that
`\angle W= 39`,
`\angle U=31`,
`VW=3.3` and
`UV=w`

Using the law of sines, we have,

`(sin U)/(3.3) =(sin W)/(w)`

Substituting the values, we have,

`(\sin 31)/(3.3)=(\sin 39)/(w)`

Cross multiplying, we get,

`(sin31) w=3.3( \sin 39)`

Simplifying, we have,

`0.515w=2.077`

Dividing both sides by 0.515, we have,

`w=4.0`

Thus, the value of w is 4.0 cm

Hence, Option B is the correct answer.