Mathematics: Find x. A. 21(route)2 B. 7 C.21(route)3/2 D. 21(route)2/2

Find x. A. 21(route)2 B. 7 C.21(route)3/2 D. 21(route)2/2

sindy35111

31.01.2022

Option (D)

Step-by-step explanation:

By applying Sine rule in the right ΔABD,

Sin(A) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

Sin(60)° = $\frac{\text{BD}}{\text{AB}}$

$\frac{\sqrt{3}}{2}=\frac{\text{BD}}{7\sqrt{3}}$

BD = $7\sqrt{3}\times \frac{\sqrt{3} }{2}$

= $\frac{21}{2}$

Now by applying Cosine rule in the right ΔBDC,

Cos(45)° = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$\frac{1}{\sqrt{2}}=\frac{\frac{21}{2}}{x}$

x = $\frac{21}{2}\times \sqrt{2}$

x = $\frac{21\sqrt{2}}{2}$

Therefore, Option (D) is the correct option.

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