Question

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

Answer 1

Answer:

XY = 4.9

Step-by-step explanation:

Answer 2

Answer:

$XY = 4.9$

Step-by-step explanation:

$\angle Y = 45^\circ$

$\angle Z = 60^\circ$

$XZ = 4$

Required

Determine the length of XY?

This question is supported with the attachment.

To solve for the length of XY, we make use of the sine law which states:

$\frac{sin\ A}{a} = \frac{sin\ B}{b} = \frac{sin\ C}{c}$

In this case:

$\frac{sin\ \angle Y}{XZ} = \frac{sin\ \angle Z}{XY} = \frac{sin\ X}{YZ}$

Substitute in, the following values:

$\angle Y = 45^\circ$

$\angle Z = 60^\circ$

$XZ = 4$

The expression becomes:

$\frac{sin\ 45}{4} = \frac{sin\ 60}{XY}$

Cross multiply

$XY * \sin\ 45 = 4 * \sin\ 60$

Make XY the subject

$\frac{XY * \sin\ 45}{\sin\ 45} = \frac{4 * \sin\ 60}{\sin\ 45}$

$XY = \frac{4 * \sin\ 60}{\sin\ 45}$

$XY = \frac{4 * 0.8660}{0.7071}$

$XY = \frac{3.4640}{0.7071}$

$XY = 4.89888276057$

$XY = 4.9$ --- approximated