Question

[Q1]
Diketahui segitiga ABC, ∠BAC = 15°, ∠ABC = 140°, dan panjang AB = 5 cm. Hitunglah panjang sisi BC, dan AC.
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Answer 1

Verified answer

Jawab:

Penjelasan dengan langkah-langkah:

Trigonometri

[tex]\frac{AB}{\sin25^\circ}=\frac{BC}{\sin15^\circ}=\frac{AC}{\sin140^\circ}\\\\[/tex]

[tex]\displaystyle\frac{AB}{\sin25^\circ}=\frac{BC}{\sin15^\circ}\\\\\frac{5}{0,42}=\frac{BC}{0,25}\\\\BC=\frac{0,25\times5}{0,42} \\\\BC=\frac{1,25}{0,42}\\\\BC\approx2,97 cm[/tex]

[tex]\displaystyle\frac{AB}{\sin25^\circ}=\frac{AC}{\sin140^\circ}\\\\\frac{5}{0,42}=\frac{AC}{0,64}\\\\AC=\frac{0,64\times5}{0,42} \\\\AC=\frac{3,2}{0,42}\\\\AC\approx7,61 cm[/tex]

Answer 2

Jawaban:

BC = 3,0621 cm

AC = 7,6048

Penjelasan dengan langkah-langkah:

diketahui ∆ ABC

<BAC = 15° = <a

<ABC = 140° = <b

<BCA = 180-(140+15) = 25° = <c

[tex] \frac{ab}{ \sin(c) } = \frac{ac}{ \sin(b) } = \frac{bc}{ \sin(a) } [/tex]

[tex] \frac{ab}{ \sin(c) } = \frac{bc}{ \sin(a) } \\ bc = \frac{ab \times \sin(a) }{ \sin(c) } \\ = \frac{5 \times \sin(15) }{ \sin(25) } \\ = 3.0621 \: \: cm[/tex]

[tex] \frac{ab}{ \sin(c) } = \frac{ac}{ \sin(b) } \\ ac = \frac{ab \times \sin(b) }{ \sin(c) } \\ = \frac{5 \times \sin(140) }{ \sin(25) } \\ = 7.6048cm[/tex]