Problem

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)

Solution

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 :\(\boxed{\angle B \approx 30^\circ}\)

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Source: https://solvelyapp.com/problems/8608/

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