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

Solution given:

Y=90°

∠X=73°.

∠ZWY=80°

and XW=80.

ZY=?

We know that

In right angled triangle ∆ XYZ

Tan 73=

3.27=

3.27×[xy]=yz

xw+wy=

wy=-80...........(1)

again

In right angled triangle WYZ

Tan 80=

5.67×wy=yz

wy=

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

Equating equation 1&2

=-80

-=80

5.67yz-3.27yz=80*5.67*3.27

2.4yz =1483.272

yz=

yz=618.03

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

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional