Question

List the sides in order from the largest to the smallest. A. XY, YW, WX B. XY, WX, YW C. WX, YW, XY D. WX, XY, YW

Answer 1

Answer:

Option (D)

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

$\frac{\text{SinW}}{\text{XY}}=\frac{\text{SinY}}{\text{XW}}=\frac{\text{SinX}}{\text{WY}}$

$\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}=\frac{\text{Sin39}}{\text{WY}}$

$\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin82}}{\text{XW}}$

$\frac{\text{XW}}{\text{XY}}=\frac{\text{Sin82}}{\text{Sin59}}$

      = 1.1489

XW : XY ≈ 1.15 : 1

$\frac{\text{Sin59}}{\text{XY}}=\frac{\text{Sin39}}{\text{WY}}$

$\frac{\text{XY}}{\text{WY}}=\frac{\text{Sin59}}{\text{Sin39}}$

$\frac{\text{XY}}{\text{WY}}=\frac{1.36}{1}$

$\frac{\text{XY}}{\text{WY}}=\frac{\frac{1}{1}}{\frac{1}{1.36} }$

$\frac{\text{XY}}{\text{WY}}=\frac{1}{0.7342}$

XY : WY = 1 : 0.7342

XW : XY : WY = 1.15 : 1 : 0.7342

Therefore, WX > XY > WY

Option (D). will be the correct option.