Anonymous
Anonymous asked in Science & MathematicsMathematics · 9 months ago

# What is the measurement of side a? Relevance

The Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle.

a^2 + 9^2 = 12^2

a^2 = 12^2 - 9^2

a^2 = 144 - 81

a^2 = 63

a = 7.94

• =sqrt(144-81) =~7.937

• a = √(144 - 81) = √63 = 3√7 = 7.937253933

• That "appears" to be a Right Angle, but that is not specified. What if it was 91 degrees???

So from the info given YOU CANNOT BE SURE OF AN ANSWER.

IF they told you it's 90 degrees (a Right Triangle), then use Pythagoras. • a²   = 12²  - 9²

a²   = (12 - 9) (12  + 9)

a²   = 3 x 21

a   = √3 x √21

a  = √63

• Use the Pythagorean Theorem.

a^2 + 9^2 = 12^2

a^2 + 81 =144

a^2 = 63

a = √63

• Using Pythagoras' theorem side 'a' is 3 times square root of 7 or about 7.94

• You have given the lengths of two sides of a triangle, but have given no angles. No, there is no right angle in the given conditions. The best we can do is this inequality.

12 - 9 < a < 12 + 9

3 < a < 21

• a = sqrt(12^2 - 9^2)

Side a = 7.94

• Hypotenuse is 12

==> 12^2 = 9^2 + a^2

==> 144 = 81 + a^2

==> 144 - 81 = a^2

==> 63 = a^2

==> a = 8( approx)