Question

in δwxy, x = 600 cm, w = 530 cm and ∠w = 111°. find all possible values of ∠x, to the nearest 10th of a degree.
answer attempt 1 out of 2
additional angle no possible angles

Explanation:

Step1: Apply the Law of Sines

By the Law of Sines, $\frac{\sin X}{x}=\frac{\sin W}{w}$.

Step2: Substitute the given values

We have $x = 600$, $w = 530$, and $\angle W=111^{\circ}$. So $\sin X=\frac{x\sin W}{w}=\frac{600\times\sin(111^{\circ})}{530}$.
First, $\sin(111^{\circ})\approx0.9336$. Then $\frac{600\times0.9336}{530}=\frac{560.16}{530}\approx1.057$.

Step3: Analyze the value of sine

Since the range of the sine - function is $[- 1,1]$, and $\sin X\approx1.057>1$, there are no possible angles for $\angle X$.

Answer:

No Possible Angles