Each leg of a 45-45-90 triangle has a length of 6 units. What is the length of its hypotenuse?

1 answer:

5 0

Use the Pythagorean theorem:
$(\hbox{one leg})^2+(\hbox{the other leg})^2=(\hbox{hypotenuse})^2 \\
6^2+6^2=x^2 \\
6^2 \times 2=x^2 \\
\sqrt{6^2 \times 2}=x \\ \sqrt{6^2} \times \sqrt{2}=x \\ 6\sqrt{2}=x
$

The length of the hypotenuse is 6√2 units.

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Step-by-step explanation:

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This question is solved using the concepts of sensitivity and specificity.

Sensitivity: It is the true negative rate, that is, the proportion of people without the disease that test negative.
Specificity: It is the true positive rate, that is, the proportion of people with the disease that test positive.

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Sensitivity of 60% means that of the 100 - 10 = 90% of people without the disease, 60% test negative and 100 - 60 = 40% test positive.
Specificity of 70% means that of the 10% with the disease, 70% test positive.

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