Question

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

Answer 1

Answer:

Solution given:

Y=90°

∠X=73°.

∠ZWY=80°

and XW=80.

ZY=?

We know that

In right angled triangle ∆ XYZ

Tan 73=$\frac{p}{h}$

3.27=$\frac{yz}{xy}$

3.27×[xy]=yz

xw+wy=$\frac{yz}{3.27}$

wy=$\frac{yz}{3.27}$-80...........(1)

again

In right angled triangle WYZ

Tan 80=$\frac{yz}{wy}$

5.67×wy=yz

wy=$\frac{yz}{5.67}$

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

Equating equation 1&2

$\frac{yz}{5.67}$=$\frac{yz}{3.27}$-80

$\frac{yz}{3.27}$-$\frac{yz}{5.67}$=80

5.67yz-3.27yz=80*5.67*3.27

2.4yz =1483.272

yz=$\frac{1483.272}{2.4}$

yz=618.03

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