Question

In ΔWXY, x = 680 inches, w = 900 inches and ∠W=157°. Find all possible values of ∠X, to the nearest degree.

Answer 1

Given:

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

To find:

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

Solution:

Law of Sines:

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

For ΔWXY,

`(w)/(\sin W)=(x)/(\sin X)=(y)/(\sin Y)`

Now,

`(w)/(\sin W)=(x)/(\sin X)`

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

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

`\sin X=(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.