Question

In ΔVWX, the measure of ∠X=90°, XW = 36, WV = 85, and VX = 77. What ratio represents the sine of ∠W?

Answer 1

Given:

In ΔVWX, the measure of ∠X=90°, XW = 36, WV = 85, and VX = 77.

We need to determine the ratio that represents the sine of ∠W

Ratio of sin of ∠W:

The ratio of sin of ∠W can be determined using the trigonometric ratios.

The ratio of
`sin \ \theta` is given by

`sin \ \theta=(opp)/(hyp)`

From the attached figure, the opposite side of ∠W is XV and the hypotenuse of ∠W is WV.

Hence, substituting in the above ratio, we get;

`sin \ W=(XV)/(WV)`

Substituting the values, we get;

`sin \ W=(77)/(85)`

Thus, the ratio of sine of ∠W is
`sin \ W=(77)/(85)`