Use the Pythaogorean Theorem to determine the exact length of AB.
Express the answer as A) an exact value in simplest mixed radical form
B) A decimal to the nearest hundredth
The picture is right here, I uploaded it of the diagram.
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In ∆ADC
AD^2 + 8^2 = 12^2
AD^2 = 80
in ∆ABD
BD^2 + AD^2 = AB^2
36 + 80 = AB^2
AB = √116 or 2√29
In order to use the Pythagorean Theorem to determine the length of AB, we need to know the lengths of the other two sides of the right triangle ABC. Unfortunately, the uploaded picture is not visible in this format, but I can still guide you on how to solve the problem.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's assume that side AC has length a, and side BC has length b. So, we have:
AC^2 + BC^2 = AB^2
If you have the lengths of AC and BC, you can plug those values into the equation and solve for AB. Once you have calculated the value of AB, you can express it in the required formats:
A) If the square root in the answer cannot be simplified, you express the answer as a mixed radical. For example, if the square root of 7 is the exact value, the answer would be √7.
B) If you need to round the answer to a decimal to the nearest hundredth, you can use a calculator to evaluate the square root and then round the decimal to the nearest hundredth.
If you provide the lengths of AC and BC, I can assist you in calculating the exact length of AB and expressing it in the required formats.