Question

What is the length of the side labeled x?

Answer 1

Answer:

AB = 42.15 units

Step-by-step explanation:

In triangle ABD,

By applying Cosine rule in this triangle,

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

$\frac{\sqrt{3} }{2}$ = $\frac{AD}{AB}$

$\frac{\sqrt{3}}{2}=\frac{AD}{47}$

AD = $\frac{47\sqrt{3}}{2}$

By applying tangent rule in ΔACD,

tan(44)° = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(44)° = $\frac{AD}{x}$

0.9657 =  $\frac{\frac{47\sqrt{3}}{2}}{x}$

0.9657 = $\frac{47\sqrt{3}}{2x}$

x = $\frac{47\sqrt{3}}{2(0.9657)}$

x = 42.15

  ≈ 42.2 units