In a right triangle, if #a=3# and #b=6#, what is the value of #c#?

Answer 1

#c=sqrt(45)#

When trying to find the area of a right triangle, we use the Pythagorean Theorem:

#color(red)a^2+color(blue)b^2=color(green)c^2#
In this case we are given the values for #color(red)a# and #color(blue)b#, so:
#(color(red)(3))^2+(color(blue)6)^2=color(green)c^2#

Which is equal to:

#(color(red)(9))+(color(blue)36)=color(green)c^2# #color(purple)45=color(green)c^2# #sqrt(color(purple)45)=sqrt(color(green)c^2)#

So:

#color(green)c=color(green)(sqrt(45)=3sqrt(5))#
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Answer 2

In a right triangle, if one leg (a) measures 3 units and the other leg (b) measures 6 units, the value of the hypotenuse (c) can be found using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

Therefore, using the Pythagorean theorem:

[ c^2 = a^2 + b^2 ]

Substituting the given values:

[ c^2 = 3^2 + 6^2 ] [ c^2 = 9 + 36 ] [ c^2 = 45 ]

Taking the square root of both sides:

[ c = \sqrt{45} ]

Therefore, the value of ( c ) is ( \sqrt{45} ) or approximately ( 6.71 ) units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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