7. In $\triangle A B C, \angle C=90^{\circ}, a=21.4 \mathrm{~cm}$, and $c=42.8 \mathrm{~cm}$. Draw a diagram to represent this triangle. Calculate $\angle B$ to the nearest degree. (K-2)
Answer
\(\boxed{\angle B \approx 30^\circ}\)
Step 1 ：Given a right triangle $\triangle ABC$ with $\angle C = 90^\circ$, $a = 21.4 \text{ cm}$, and $c = 42.8 \text{ cm}$.
Step 2 ：Since it's a right triangle, we can use the sine function to find $\angle B$. The sine function is defined as $\sin(\text{angle}) = \frac{\text{opposite side}}{\text{hypotenuse}}$. In this case, $\sin(B) = \frac{a}{c}$.
Step 3 ：Calculate the value of $\sin(B)$: $\sin(B) = \frac{21.4}{42.8} = 0.5$.
Step 4 ：Use the inverse sine function (arcsin) to find $\angle B$: $\angle B = \arcsin(0.5) \approx 30^\circ$.
Step 5 ：\(\boxed{\angle B \approx 30^\circ}\)
