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 to find $\sin B$

The Law of Sines states $\frac{a}{\sin A} = \frac{b}{\sin B}$. Rearranging to solve for $\sin B$ gives $\sin B = \frac{b \sin A}{a}$.
Substitute $a=22$, $A=117^\circ$, $b=34$:
$\sin B = \frac{34 \sin(117^\circ)}{22}$
First calculate $\sin(117^\circ) = \sin(180^\circ-63^\circ) = \sin(63^\circ) \approx 0.8910$
Then $\sin B \approx \frac{34 \times 0.8910}{22} \approx \frac{30.294}{22} \approx 1.377$

Step2: Analyze validity of $\sin B$

The range of the sine function is $-1 \leq \sin x \leq 1$. Since $\sin B \approx 1.377 > 1$, no such angle $B$ exists.

Answer:

0