Question

a $sin(37)=\frac{10.3}{x}$
b $sin(37)=\frac{x}{10.3}$
c $sin(x)=\frac{37}{10.3}$
(b) find the value of x (round to two decimal places, show all work:
17.12

Explanation:

Step1: Recall sine - definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Given an angle of $37^{\circ}$, if the opposite side to the $37^{\circ}$ angle is $x$ and the hypotenuse is $10.3$, then $\sin(37)=\frac{x}{10.3}$. So the correct option for part (a) is B.

Step2: Solve for $x$

We know that $\sin(37)=\frac{x}{10.3}$. Since $\sin(37)\approx0.6018$, we can rewrite the equation as $0.6018=\frac{x}{10.3}$.

Step3: Isolate $x$

Multiply both sides of the equation by $10.3$: $x = 10.3\times\sin(37)$.
$x=10.3\times0.6018 = 6.19854\approx6.20$.

Answer:

(a) B. $\sin(37)=\frac{x}{10.3}$
(b) $6.20$