Question

In ΔXYZ, ∠Y=90° and ∠X=73°. ∠ZWY=80° and XW=80. Find the length of ZY to the nearest 100th.

Answer 1

Solution given:

Y=90°

∠X=73°.

∠ZWY=80°

and XW=80.

ZY=?

We know that

In right angled triangle ∆ XYZ

Tan 73=
`(p)/(h)`

3.27=
`(yz)/(xy)`

3.27×[xy]=yz

xw+wy=
`(yz)/(3.27)`

wy=
`(yz)/(3.27)`-80...........(1)

again

In right angled triangle WYZ

Tan 80=
`(yz)/(wy)`

5.67×wy=yz

wy=
`(yz)/(5.67)`

yz=5.67×wy............................................(2)

Equating equation 1&2

`(yz)/(5.67)`=
`(yz)/(3.27)`-80

`(yz)/(3.27)`-
`(yz)/(5.67)`=80

5.67yz-3.27yz=80*5.67*3.27

2.4yz =1483.272

yz=
`(1483.272)/(2.4)`

yz=618.03

:.y=618.03unit.the length of ZY to the nearest 100th is 618.