The value of < ABC in Δ ABC is 45 derajat. if < CAB = 105 derajat and AC = 15, the length of AB = .... Question from @Bellasyahira

October 2018 2 79 Report

The value of < ABC in Δ ABC is 45 derajat. if < CAB = 105 derajat and AC = 15 $\sqrt{2} cm$ , the length of AB = .... cm
a. 15
b. $15 \sqrt{2}$
c. 30
d. $30 \sqrt{2}$
e. 45

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ekamiaww < A + < B + < C = 180°
105° + 45° + < C = 180°
< C = 180° - 150°
< C = 30°

dgn aturan sinus
$\displaystyle\ \frac{AB}{\sin C}= \frac{AC}{\sin B} \\ \frac{AB}{\sin 30^o}= \frac{15 \sqrt{2} }{\sin 45^o} \\ \frac{AB}{ \frac{1}{2} }= \frac{15 \sqrt{2} }{\frac{1}{2} \sqrt{2} } } \\ AB=15\ cm$

semoga membantu ya :)

0 votes Thanks 0

alvinteguh < C = 180 - 45 - 105 = 30
AC / sin B = AB / sin C
15√2 / sin 45 = AB / sin 30
15√2 / 1/2√2 = AB / 1/2
30 = 2AB
AB = 15 cm

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