# Solve the right triangle: X=35(degrees) side x=5

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### 1 Answer

Let our triangle be XYZ, where Z is the right angle.

So we have,

`X = 35^o` `barx = 5`

`Z = 90^o ` `barz` is the hypotenuse

Note that in a triangle the sum of the interior angles is `180^o` . So, Y is:

`X+Y+Z= 180`

`35 + Y + 90 = 180`

`Y+125 = 180`

` Y = 180 -125`

` Y = 55`

Hence, angle `Y = 55^o` .

To solve for the other two sides of the triangle, we may use sine and tangent function.

`tan theta = (opposite)/(adjacent)` `sin theta = (opposite)/(hypoten use)`

`tan X = (barx)/(bary) ` `sin X = (barx)/(barz) `

`tan 35 = 5 / (bar y) ` `sin 35 = 5/(barz) `

`bary = 5/(tan 35) ` `barz = 5/(sin35)`

`bary= 7.1 ` `barz = 8.7`

**Hence, angles of the right triangle are:**

** `X= 35^o` `Y = 55^o ` and `Z =90^o` **

**And the length of the sides opposite to each angle above are:**

** `barx=5 ` **units ** `bary = 7.1` **units** and `barz=8.7` **units