Find the lengths of the missing sides in the triangle. Write your answers as integers or as decimals rounded to the nearest tenth.

Answer:

[tex]x = 9.9[/tex]

[tex]y= 7[/tex]

Step-by-step explanation:

Given

See attachment for triangle

Required

Find x and y

Considering  [tex]\theta = 45[/tex]

From the attached triangle, length x is the hypotenuse and length y is the adjacent

Solving for x

[tex]Sin\theta = \frac{Opp}{Hyp}[/tex]

[tex]Sin\theta = \frac{7}{x}[/tex]

So, we have:

[tex]Sin45 = \frac{7}{x}[/tex]

[tex]x= \frac{7}{Sin45 }[/tex]

[tex]x = \frac{7}{0.7071}[/tex]

[tex]x = 9.9[/tex]

Solving for y

Considering  [tex]\theta = 45[/tex]

[tex]Tin\theta = \frac{Opp}{Adj}[/tex]

So, we have:

[tex]Tin45= \frac{7}{y}[/tex]

[tex]y= \frac{7}{Tan45}[/tex]

[tex]y= \frac{7}{1}[/tex]

[tex]y= 7[/tex]

The value of x and y is 9.9 and 7.

Since theta is 45 degrees

So, we know that

Sin theta = opp/hyp

Sin theta = 7 /x

x = 7 / 0.7071

= 9.9

Now the value of Y should be

Tin theta = opp/hyp

y = 7 \tan 45

= 7 /1

= 7

Therefore, we can conclude that The value of x and y is 9.9 and 7.

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