Given △XYZ , m∠X=38∘ , m∠Z=67∘ , and YZ=25 feet . we need to find XZ.
Two angles and one side is given to us.
In any triangle sum of angles =180°
In triangle XYZ,<X+<Y+<Z=180°
Or 38+<Y+67 = 180
< Y+105= 180°
<Y = 75°
We can apply sine rule to find XZ
The sine Rule states in any triangle ABC ,
[tex] \frac{Sin A}{a} =\frac{Sin B}{b} =\frac{SinC}{c} [/tex]
Applying the rule to triangle XYZ to find XZ we have:
[tex] \frac{Sin 38}{25} =\frac{Sin 75 }{XZ} [/tex]
Cross multiplying we have:
XZ .Sin 38= 25 .Sin75
Substituting Sin38 and Sin 75 values we have:
XZ(0.62)= 25(0.97)
0.62 XZ= 24.15
XZ= 38.94 feet.
