Question

consider a triangle (abc) like the one below. suppose that (b = 45), (c = 69), and (b = 97^circ). (the figure is not drawn to scale.) solve the triangle.

carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.

if no such triangle exists, enter
o solution.\ if there is more than one solution, use the button labeled \or\.

(c = \box^circ), (a = \box^circ), (a = \box)

Explanation:

Set up the Law of Sines relation

Using the Law of Sines knowledge point

$$ \frac{\sin B}{b} = \frac{\sin C}{c} $$

Substitute the given values

Using the Law of Sines knowledge point

$$
LATEXBLOCK0
$$

Solve for the sine of angle C

Using the Law of Sines knowledge point

$$
LATEXBLOCK1
$$

Analyze the existence of solutions

Using the Ambiguous Case of Law of Sines knowledge point

$$
LATEXBLOCK2
$$

Answer:

Consider a triangle \(ABC\) like the one below. Suppose that \(b = 45\), \(c = 69\), and \(B = 97^\circ\). Solve the triangle.

If no such triangle exists, enter "No solution."

<blank>No solution</blank>