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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:
`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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