# If c is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth if necessary. a=?,b=15,c=31

Note that the angle opposite to hypotenuse is always 90 degrees. Base on this, it indicates that a, b and c are the sides of a right triangle.

So to solve for a, apply the Pythagorean formula which is:

`c^2=a^2+b^2`

where c is the hypotenuse, and the legs of the...

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Note that the angle opposite to hypotenuse is always 90 degrees. Base on this, it indicates that a, b and c are the sides of a right triangle.

So to solve for a, apply the Pythagorean formula which is:

`c^2=a^2+b^2`

where c is the hypotenuse, and the legs of the right triangle are a and b.

Plug-in c=31 and b=15 to the formula.

`31^2=a^2+15^2`

`961=a^2+225`

Subtract both sides by 225.

`961-225=a^2+225-225`

`736=a^2`

And take the square root of both sides.

`+-sqrt736=sqrt(a^2)`

`+-27.1=a`

Since a represents the length of the triangle, take only the positive value.

Hence, `a = 27.1` .

Approved by eNotes Editorial Team