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Elden [556K]
2 years ago
9

Can someone help me on this question?

Mathematics
1 answer:
notsponge [240]2 years ago
3 0

Answer:

x = 19.6

Step-by-step explanation:

By applying cosine rule in ΔBCD,

cos(30)° = \frac{\text{Adjacent side}}{\text{Hypotenuse}}

              = \frac{BC}{BD}

\frac{\sqrt{3}}{2}=\frac{BC}{16}

BC = 8\sqrt{3}

Now, by applying sine rule in ΔBAC,

sin(45)° = \frac{\text{Opposite side}}{\text{Hypotenuse}}

\frac{1}{\sqrt{2}}=\frac{AB}{BC}

\frac{1}{\sqrt{2}}=\frac{x}{8\sqrt{3}}

x = 8\sqrt{6}

x = 19.59

x ≈ 19.6  

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