Question

In ΔVWX, x = 77 cm, ∠X=74° and ∠V=16°. Find the length of w, to the nearest 10th of a centimeter.

Answer 1

The length of w is 50.0 cm.

Explanation:

To find the length of w, we can use the Law of Sines:

w / sin V = x / sin X

Plugging in the values given in the question, we get:

w / sin 16° = 77 cm / sin 74°

Solving for w, we get:

w = 50.0 cm

Rounding to the nearest 10th of a centimeter, we get:

w = 50.0 cm

Therefore, the length of w is 50.0 cm.

Answer 2

w=80.1 cm

Explanation:

According to the Law of Sines:

`(\sin(\alpha))/(a)=(\sin(\beta))/(b)=(\sin(C))/(c)`

For this problem, let

`\alpha`=∠X=74°

`\beta`=∠V=16°

Since the sum of the angle measures in all triangles must equal 180°, ∠w must equal 90°. So, for this problem, let

C=∠W=90°.

And let

a=x=77 cm

c=w

So,

`(\sin(74))/(77\ cm)=(\sin(90))/(w)\\0.01248\ cm=(1)/(w)\\w=80.1\ cm`

This can be checked using the Law of Sines with all values entered.

To find b, use the Pythagorean Theorem:

`(80.1\ cm)^2=(77\ cm)^2+b^2\\6416.01\ cm^2=5929\ cm^2+b^2\\487.01\ cm^2=b^2\\b=22.07\ cm`

So,

`(\sin(74))/(77\ cm)=(\sin(16))/(22.07\ cm)=(\sin(90))/(80.1\ cm)\\0.0125\ cm=0.0125\ cm=0.0125\ cm`