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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lemjay's profile pic

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

Posted on

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` . 

americamom73's profile pic

americamom73 | Elementary School Teacher | eNotes Newbie

Posted on

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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