Question

in δopq, o = 9.2 inches, q = 7.4 inches and ∠q = 24°. find all possible values of ∠o, 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, $\frac{\sin O}{o}=\frac{\sin Q}{q}$. Substitute $o = 9.2$, $q = 7.4$, and $\angle Q = 24^{\circ}$ into the formula: $\sin O=\frac{o\sin Q}{q}=\frac{9.2\times\sin24^{\circ}}{7.4}$.

Step2: Calculate $\sin O$ value

First, find $\sin24^{\circ}\approx0.4067$. Then $\frac{9.2\times0.4067}{7.4}=\frac{3.74164}{7.4}\approx0.5056$. So $\sin O\approx0.5056$.

Step3: Find the principal - value of $\angle O$

Using the inverse - sine function, $O_1=\sin^{-1}(0.5056)\approx30.4^{\circ}$.

Step4: Find the additional value of $\angle O$

The sine function has a period of $360^{\circ}$, and in the range $0^{\circ}

Answer:

$30.4^{\circ},149.6^{\circ}$