Question

In triangle XYZ, angle Y = 45º and angle Z = 60º. If XZ = 4, then what is XY?

Answer 1

`XY = 4.9`

Explanation:

Given

`XZ= 4`

`\angle Y = 45`

`\angle Z = 60`

Required

Determine the measure of side XY

To do this, we make use of sine law. This is as follows:

`(a)/(\sin\ A) = (b)/(\sin\ B) = (c)/(\sin\ C)`

In this case:

`(4)/(\sin(45)) = (XY)/(\sin(60))`

Cross Multiply

`XY * \sin(45) = 4 * \sin(60)`

`XY * 0.7071 = 4 * 0.8660`

Make XY the subject

`XY = (4 * 0.8660)/(0.7071)`

`XY = (3.4640)/(0.7071)`

`XY = 4.89888276057`

`XY = 4.9` -- approximated