If c is the measure of the hypotenuse, find each missing measure. Round to the nearest tenth if necessary. a=?,b=15,c=31
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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` .
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Hi! This one may seem tricky, but math is a lot like following a recipe, adding the numbers in (ingredients) and the outcome is the answer.
To figure out this a equation you use the Pythagorean Therorem (a2+ b2= c2) and a little algebra. C is always the measure of the hypotenuse. Let's plug in what we do know.
a2 + 15*15 = 31*31
a2 + 225 = 961
a2 + 225-225= 961 - 225
a2 = 736
then you must find the square root of 736 with your calculator.
a= 27.1293199 then round this number to the nearest 10th.
a= 27.1
I hope this helps.
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