Question

Find the measure of Angel A? (Round your answer to the nearest whole number)

Answer 1

Concept:

To figure out the measure of angle A, we will use the sine rule below

`\begin{gathered} (a)/(sinA)=(b)/(sinB)=(c)/(sinC) \\ where, \\ a=37cm \\ c=29cm \\ C=50^0 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} (a)/(sinA)=(c)/(sinC) \\ (37)/(sinA)=(29)/(sin50^0) \\ \end{gathered}`

Cross multiply, we will have

`\begin{gathered} (37)/(s\imaginaryI nA)=(29)/(s\imaginaryI n50^0) \\ 29\sin A=37* sin50^0 \\ sinA=(37sin50^0)/(29) \\ sinA=0.9774 \\ find\text{ the arcsin} \\ A=\sin^(-1)0.9774 \\ A=77.79^0 \\ A\approx78^0(nearest\text{ whole number\rparen} \end{gathered}`

Hence,

The measure of angle A to the nearest whole number is

`\Rightarrow78^0`