Question

in △vwx, w = 700 inches, v = 690 inches and ∠v = 74°. find all possible values of ∠w, to the nearest degree.

Explanation:

Step1: Apply the Law of Sines

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

Step2: Substitute the given values

We have $w = 700$, $v=690$, and $V = 74^{\circ}$. So $\sin W=\frac{w\sin V}{v}=\frac{700\times\sin74^{\circ}}{690}$.
First, calculate $\sin74^{\circ}\approx0.9613$. Then $\frac{700\times0.9613}{690}=\frac{672.91}{690}\approx0.9752$.

Step3: Find the principal - value of angle W

$W=\sin^{- 1}(0.9752)$. Using a calculator, $W_1=\sin^{-1}(0.9752)\approx77^{\circ}$.

Step4: Find the additional angle

Since $\sin\theta=\sin(180^{\circ}-\theta)$, the additional angle $W_2 = 180^{\circ}-77^{\circ}=103^{\circ}$.

Answer:

$77^{\circ},103^{\circ}$