Respuesta :
Answer:
Given: A = 72°, a = 34, b = 21
Calculated: B = 35.97°, C = 72.03°, c = 34.00
Step-by-step explanation:
[tex] \dfrac{\sin A}{a} = \dfrac{\sin B}{b} [/tex]
[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin B}{21} [/tex]
[tex] \sin B = \dfrac{21\sin 72^\circ}{34} [/tex]
[tex] \sin B = 0.5874 [/tex]
[tex] B = \sin^{-1} 0.5874 [/tex]
[tex] B = 35.97^\circ [/tex]
C = 180° - 72° - 35.97°
C = 72.03°
[tex] \dfrac{\sin A}{a} = \dfrac{\sin C}{c} [/tex]
[tex] \dfrac{\sin 72^\circ}{34} = \dfrac{\sin 72.03^\circ}{c} [/tex]
[tex]c = \dfrac{\sin 72.03^\circ \times 34}{\sin 72^\circ}[/tex]
[tex] c = 34.00 [/tex]
Given: A = 72°, a = 34, b = 21
Calculated: B = 35.97°, C = 72.03°, c = 34.00
Answer:
[tex]B\approx35.97^\circ\\C\approx72.03^\circ\\c\approx34[/tex]
Step-by-step explanation:
Law of Sines
[tex]\frac{sinA}{a}=\frac{sinB}{b}=\frac{sinC}{c}[/tex]
Given information
[tex]A=72^\circ\\a=34\\b=21[/tex]
Check if solutions exist
As [tex]A=72^\circ < 90^\circ[/tex] and that [tex]a > b\rightarrow 34 > 21[/tex], then there exists only one possible triangle by the Ambiguous Case
Solve the triangle
[tex]\frac{sin(72^\circ)}{34}=\frac{sin(B)}{21}\\ \\ 21sin(72^\circ)=34sin(B)\\\\\frac{21sin(72^\circ)}{34}=sin(B)\\ \\B=sin^{-1}(\frac{21sin(72^\circ)}{34})\\ \\B=35.97394255^\circ\approx35.97^\circ[/tex]
[tex]A+B+C=180^\circ\\\\72^\circ+35.97394255^\circ+C=180^\circ\\\\107.97394255^\circ+C=180^\circ\\\\C=72.02605745^\circ\approx72.03^\circ[/tex]
[tex]\frac{sin(72^\circ)}{34}=\frac{sin(72.02605745^\circ)}{c}\\\\c*sin(72^\circ)=34sin(72.02605745^\circ)\\\\c=\frac{34sin(72.02605745^\circ)}{sin(72^\circ)}\\ \\c=34.00502065\approx34[/tex]
