Use the information below to find the missing measure such that .
AB = 35, DE = 14, DF = 22, , AC = ?
Assuming you have two triangles where ΔABC~ΔDEF, then
AC/DF = AB/DE
or
AC=(AB/DE)*DF
=(35/14)*22
=55
To find the missing measure AC, we can use the theorem of Pythagoras, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, we have triangle ADF, with sides AD, DF, and AF. We are given the lengths of AD and DF, and we need to find the length of AF, which is AC in this case.
Applying the Pythagorean theorem, we have:
AD^2 + DF^2 = AF^2
Substituting the given values, we get:
35^2 + 22^2 = AF^2
Simplifying further:
1225 + 484 = AF^2
1709 = AF^2
To find the value of AF, we can take the square root of both sides:
√1709 = AF
Calculating the square root of 1709, we find that AF is approximately equal to 41.36.
Therefore, the missing measure AC is approximately 41.36.