Question

question 20 (5 points) listen how many triangles are there that satisfy the conditions a = 13, b = 6, α = 6°? 1 0 2 impossible to determine

Explanation:

Step1: Apply the Law of Sines

By the Law of Sines, $\frac{a}{\sin\alpha}=\frac{b}{\sin\beta}$, so $\sin\beta=\frac{b\sin\alpha}{a}$.
Substitute $a = 13$, $b = 6$, and $\alpha=6^{\circ}$ into the formula: $\sin\beta=\frac{6\sin6^{\circ}}{13}$.

Step2: Calculate the value of $\sin\beta$

We know that $\sin6^{\circ}\approx0.1045$, then $\sin\beta=\frac{6\times0.1045}{13}=\frac{0.627}{13}\approx0.0482$.
Since $0<\sin\beta\approx0.0482 < 1$, and $a>b$, there is 1 triangle.

Answer:

1