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

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lemjay | High School Teacher | (Level 3) Senior Educator

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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

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