Question

in ∆xyz, angle y =90°, angle z=45° if xz=3√2 then find 2yandxy​

Answer 1

Answer:

In △XYZ,∠Y=90

o

,∠Z=a

o

and ∠X=(a+30)

o

XZ=24 ...... (Given)

In triangle XYZ,

∠X+∠Y+∠Z=180

o

⟹(a+30)

o

+90

o

+a

o

=180

o

⟹2a=60

o

⟹a=30

o

∴∠Z=30

o

and ∠Y=60

o

Now, sin30

o

=

XZ

XY

⟹

2

1

=

24

XY

⟹XY=12 cm

Also, cos30

o

=

XZ

YZ

⟹

2

3

=

24

YZ

⟹YZ=12

3

cm

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Answer 2

Given:

∆xyz

angle y =90°

angle z=45

XZ=3√2

Find ZY and XY=?

∠X + ∠Y + ∠Z = 180°

∠X + 90° + 45° = 180°

∠X + 135° = 180°

∠X = 180° - 135°

∠X = 45°

$sin45\°=\frac{XY}{XZ}$

$\frac{1}{\sqrt{2} } = \frac{XY}{3\sqrt{2} }$

$XY=\frac{3\sqrt{2} }{\sqrt{2} }$

XY=3

$cos45\° =\frac{YZ}{XZ}$

$\frac{1}{\sqrt{2} } = \frac{YZ}{3\sqrt{2} }$

$YZ=\frac{3\sqrt{2} }{\sqrt{2} }$

YZ=3

Hence the answer is XY and YZ is 3