Question

m∠c = 36°, ab = 31, bc = 24, find m∠a. m∠a =

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that $\frac{AB}{\sin C}=\frac{BC}{\sin A}$.

Step2: Substitute the given values

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

Step3: Solve for $\sin A$

Cross - multiply to get $31\sin A=24\sin36^{\circ}$. Then $\sin A=\frac{24\sin36^{\circ}}{31}$.
We know that $\sin36^{\circ}\approx0.5878$, so $\sin A=\frac{24\times0.5878}{31}=\frac{14.1072}{31}\approx0.4551$.

Step4: Find the measure of angle $A$

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

Answer:

$27$