Paul sketches a right triangle with legs of length a and b and a hypotenuse of length h. He writes an equation that relates lengths a, b, and h. Then he writes an expression for the length of the hypotenuse. Which equation does he write?
√a^2 - b^2
√a+b
√a-b
√a^2 + b^2
none of them, unless you meant to type
√(a^2 + b^2)
And your answer is?
that's what I meant on the last one, is it right?
Does the answer choice have the parentheses?
No, but I think it is probably supposed to.
Is there a difference between √a^2 + b^2 and √ (a^2 + b^2)
in your text, probably not, since the radical bar extends over the whole expression. Since we can't show that online, it's always best to use the parentheses. Otherwise, the order of operations demands that it be parsed as
(√a^2) + b^2
because powers are done before addition.
ok thank you very much
To determine which equation Paul writes to relate the lengths a, b, and h in a right triangle, we need to consider the Pythagorean theorem. The Pythagorean theorem states that, in a right triangle, the square of the length of the hypotenuse (h) is equal to the sum of the squares of the lengths of the two legs (a and b).
Using this information, we can eliminate the equation √a+b since it does not account for the squares of a and b. Likewise, we can eliminate √a-b since it subtracts b^2 instead of adding it.
Therefore, the correct equation that Paul writes to relate a, b, and h is √a^2 + b^2. This equation represents the Pythagorean theorem and is used to find the length of the hypotenuse when given the lengths of the legs.