find the measure of the acute angle, $x$, in degrees. the figure is drawn to scale. round to the hundredths…
find the measure of the acute angle, $x$, in degrees. the figure is drawn to scale. round to the hundredths place.\nshow your work here
Answer
Explanation:
Step1: Identify the Law of Sines
$$\frac{a}{\sin(A)} = \frac{b}{\sin(B)}$$
Step2: Substitute the given values
$$\frac{15}{\sin(x)} = \frac{7}{\sin(26^{\circ})}$$
Step3: Solve for $\sin(x)$
$$\sin(x) = \frac{15 \cdot \sin(26^{\circ})}{7}$$
Step4: Calculate the value of $\sin(x)$
$$\sin(x) \approx \frac{15 \cdot 0.43837}{7} \approx 0.93937$$
Step5: Find the inverse sine
$$x = \arcsin(0.93937)$$
Step6: Calculate the angle in degrees
$$x \approx 69.948^{\circ}$$
Step7: Round to the hundredths place
$$x \approx 69.95^{\circ}$$
Answer:
69.95^{\circ}