Question

question 19 of 20
how many solutions does a triangle with values a = 22, a = 117°, and b = 34 have?
write your answer in numeric form.

Explanation:

Step1: Apply Law of Sines

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

Step2: Solve for $\sin B$

$\sin B = \frac{b \sin A}{a} = \frac{34 \sin 117^\circ}{22}$

Step3: Calculate $\sin 117^\circ$

$\sin 117^\circ = \sin(63^\circ) \approx 0.8910$

Step4: Compute $\sin B$ value

$\sin B \approx \frac{34 \times 0.8910}{22} \approx \frac{30.294}{22} \approx 1.377$

Step5: Analyze validity of $\sin B$

Since the range of sine function is $[-1, 1]$, $\sin B \approx 1.377$ is impossible.

Answer:

0