Question

in xyz, <X =90,<z= 45 ,<y= 45 and xy5 root2 them find zy​

Answer 1

Answer:

In ∆XYZ,

angle Y=90°........ given

By Pythagoras' theorem,

\begin{gathered}{xy}^{2} + {yz}^{2} = x {z}^{2} \\ \\ {5}^{2} + y {z}^{2} = (5 \sqrt{2} {) }^{2} \\ \\ 25 + y {z }^{2} = 25 \times 2 \\ \\ 25+ y {z}^{2} = 50 \\ \\ y {z}^{2} = 50 - 25 \\ \\ y {z}^{2} = 25 \\ \\ yz = 5\end{gathered}

xy

2

+yz

2

=xz

2

5

2

+yz

2

=(5

2

)

2

25+yz

2

=25×2

25+yz

2

=50

yz

2

=50−25

yz

2

=25

yz=5

So in this ∆XYZ

Side XY= Side YZ

angle X= angle Z....................by isosceles triangle theorem ......1

Thus,. angle X = angle Z = x...............say

angle X + angle Y + angle Z = 180°................angle sum property

of triangle.

x + 90 + x = 180

x + x= 180-90

2x = 90

x =90/2

x=45°

angle X = angle Z = 45°

angle Y = 90°

ANS:-. The angles of the given triangle are

angle Y = 90°

angle X = 45°

angle Z = 45°