Question

in triangle xyz ,90 degree at y, if xy=5cm & xz=5√2cm, then find angle x and angle z

Answer 1

here is your answer is 45

Answer 2

In ∆XYZ,

angle Y=90°........ given

By Pythagoras' theorem,

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

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°