Question

answer the following questions. make sure to explain all your work and show all your steps.
problem #1:
solve triangle abc if a = 50°, a = 10, and b = 20. if no triangle exists, explain why.

Explanation:

Step1: Apply Law of Sines

$\frac{\sin B}{b} = \frac{\sin A}{a}$

Step2: Substitute given values

$\sin B = \frac{b \cdot \sin A}{a} = \frac{20 \cdot \sin 50^\circ}{10}$

Step3: Calculate $\sin B$ value

$\sin B = 2 \cdot \sin 50^\circ \approx 2 \cdot 0.7660 = 1.532$

Step4: Analyze sine range

The range of $\sin x$ is $[-1, 1]$. Since $1.532 > 1$, no such angle $B$ exists.

Answer:

No triangle exists because the calculated value of $\sin B \approx 1.532$, which is outside the valid range of $[-1, 1]$ for the sine function.