Answer:
Step-by-step explanation:
It is given that in ΔABC, [tex]AB=5\sqrt{2}[/tex], ∠A=45°, ∠C=30°.
Now, using the angle sum property in ΔABC, we have
[tex]{\angle}A+{\angle}B+{\angle}C=180[/tex]
[tex]45+{\angle}B+30=180[/tex]
[tex]{\angle}B=105^{\circ}[/tex]
Using the sine law, we have
[tex]ABsinC=BCsinA[/tex]
Substituting the given values, we have
[tex]5\sqrt{2}{\times}\frac{1}{2}=BC{\times}\frac{1}{\sqrt{2}}[/tex]
[tex]\frac{5}{2}=\frac{BC}{2}[/tex]
[tex]BC=5[/tex]
Again using sine law, we have
[tex]BCsinA=ACsinB[/tex]
Substituting the values, we have
[tex]5{\times}\frac{1}{\sqrt{2}}=AC{\times}sin105[/tex]
[tex]\frac{5}{1.365}=AC[/tex]
[tex]AC=3.66[/tex]
Therefore, the value of BC and AC are [tex]5[/tex] and [tex]3.66[/tex].
