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

Based on this information, the correct order of the sides from largest to smallest would be:

D. WX, XY, YW

How to determine the order of the sides in triangle WXY

To determine the order of the sides in triangle WXY based on the given angle measurements, use the angle-side relationship in triangles.

According to this relationship, the largest angle is opposite the longest side, and vice versa.

Given that angle W is 59 degrees, angle X is 39 degrees, and angle Y is 82 degrees, we can conclude the following:

Angle Y is the largest angle (82 degrees), so it is opposite the longest side. WX

Angle X is the smallest angle (39 degrees), so it is opposite the shortest side. YW

Based on this information, the correct order of the sides from largest to smallest would be:

D. WX, XY, YW

Therefore, the correct option is D.

Answer 2

Option (D)

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}}=(1.36)/(1)`

`\frac{\text{XY}}{\text{WY}}=((1)/(1))/((1)/(1.36) )`

`\frac{\text{XY}}{\text{WY}}=(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.