Question

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

[asy]
unitsize(3 cm);

pair X, Y, Z;

X = (0,1);
Y = (-1,0);
Z = (1/sqrt(3),0);

draw(X--Y--Z--cycle);

label("$45^\circ$", Y + (0.3,0.1), fontsize(10));
label("$60^\circ$", Z + (-0.2,0.1), fontsize(10));
label("$X$", X, N);
label("$Y$", Y, SW);
label("$Z$", Z, SE);
label("$4$", (X + Z)/2, NE);
[/asy]

Answer 1

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

Answer 2

Answer:

XY = 4.9

Step-by-step explanation: