Import favorites $\newline$ MVNU Students Ho... $\newline$ A $\newline$ ALEKS - Jameson C... $\newline$ Triangles and Vectors $\newline$ Solving a triangle with the law of sines: Problem type $2$ $\newline$ Jameson $\newline$ Español $\newline$ Consider a triangle $A B C$ like the one below. Suppose that $a=46, c=12$ , and $A=97^{\circ}$ . (The figure is not drawn to scale.) Solve the triangle. $\newline$ Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth. $\newline$ If no such triangle exists, enter

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MVNU Students Ho...

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ALEKS - Jameson C...

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Triangles and Vectors

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Solving a triangle with the law of sines: Problem type

2

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Jameson

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Español

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Consider a triangle

A B C

like the one below. Suppose that

a=46, c=12

, and

A=97^{\circ}

. (The figure is not drawn to scale.) Solve the triangle.

\newline

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

\newline

If no such triangle exists, enter

Find Angle C: Use the Law of Sines to find angle C. $\newline$ $\frac{\sin(C)}{c} = \frac{\sin(A)}{a}$ $\newline$ $\frac{\sin(C)}{12} = \frac{\sin(97°)}{46}$ $\newline$ $\sin(C) = \left(\frac{\sin(97°)}{46}\right) * 12$ $\newline$ Calculate $\sin(C)$ .
Calculate $\sin(C)$ : $\sin(C) = (\sin(97°)/46) \times 12$ $\newline$ $\sin(C) \approx (0.9986/46) \times 12$ $\newline$ $\sin(C) \approx 0.2604$ $\newline$ Find angle $C$ by taking the inverse sine of $0.2604$ .
Check Angle C Validity: $C = \sin^{-1}(0.2604)$ $\newline$ $C \approx 15.2^\circ$ $\newline$ Check if angle C is valid, it should be less than $180^\circ - A$ .
Find Angle B: Since $A = 97°$ , $C$ should be less than $180° - 97°$ . $\newline$ $C = 15.2°$ is valid because it's less than $83°$ . $\newline$ Now find angle $B$ using the fact that the sum of angles in a triangle is $180°$ . $\newline$ $B = 180° - A - C$
Check Angle B Validity: $B = 180° - 97° - 15.2°$ $\newline$ $B \approx 67.8°$ $\newline$ Check if angle B is valid, it should be greater than $0°$ and less than $180°$ .
Find Side b: Since $B \approx 67.8^\circ$ , it is valid. $\newline$ Now use the Law of Sines to find side $b$ . $\newline$ $\frac{\sin(B)}{b} = \frac{\sin(A)}{a}$ $\newline$ $b = a \cdot \left(\frac{\sin(B)}{\sin(A)}\right)$ $\newline$ Calculate $b$ .
Calculate $b$ : $b = 46 \times (\sin(67.8^\circ)/\sin(97^\circ))$ $b \approx 46 \times (0.9235/0.9986)$ $b \approx 42.6$ Check if side $b$ is valid, it should be greater than $0$ .