Answer:
The correct option is Second one X = 28.6°, Y = 31.2°, Z= 120.2
Therefore,
∠X = 28.6° , ∠Y = 31.2°, and ∠Z =120.2°
Step-by-step explanation:
Given:
In Δ XYZ such that Sides opposite to ∠X, ∠Y, and ∠Z are
x = 8.3 meters
y = 9 meters
z = 15 meters,
To Find:
∠X = ? , ∠Y = ?, and ∠Z = ?
Solution:
Cosine Rule In XYZ is given as
[tex]\cos X =\dfrac{y^{2}+ z^{2}-x^{2}}{2\times y\times z}[/tex]
[tex]\cos Y =\dfrac{x^{2}+ z^{2}-y^{2}}{2\times x\times z}[/tex]
[tex]\cos Z =\dfrac{x^{2}+ y^{2}-z^{2}}{2\times x\times y}[/tex]
Substituting the given values in above formula we get
[tex]\cos X =\dfrac{9^{2}+ 15^{2}-8.3^{2}}{2\times 9\times 15}=0.8781\\\\X=cos^{-1}(0.8781)=28.6\°[/tex]
Similarly for Y
[tex]\cos Y =\dfrac{8.3^{2}+ 15^{2}-9^{2}}{2\times 8.3\times 15}=0.8549\\\\Y=cos^{-1}(0.8549)=31.2\°[/tex]
Similarly For Z
[tex]\cos Z =\dfrac{8.3^{2}+ 9^{2}-15^{2}}{2\times 8.3\times 9}=-0.5027\\\\Z=cos^{-1}(-0.5027)=120.2\°[/tex]
Therefore,
∠X = 28.6° , ∠Y = 31.2°, and ∠Z =120.2°
