Question

3 fill in the blank 1 point
$mangle c = 36^{circ}, ab = 31, bc = 24$, find $mangle a$.
$mangle a=
previous

Explanation:

Step1: Apply the Law of Sines

By the Law of Sines, $\frac{BC}{\sin A}=\frac{AB}{\sin C}$.

Step2: Substitute the given values

We know $BC = 24$, $AB = 31$, and $C=36^{\circ}$. So $\frac{24}{\sin A}=\frac{31}{\sin36^{\circ}}$.

Step3: Solve for $\sin A$

$\sin A=\frac{24\sin36^{\circ}}{31}$. Calculate $\sin36^{\circ}\approx0.5878$, then $\sin A=\frac{24\times0.5878}{31}\approx\frac{14.1072}{31}\approx0.4551$.

Step4: Find the angle $A$

$A=\sin^{- 1}(0.4551)\approx27^{\circ}$.

Answer:

$27^{\circ}$