Final answer:
The measure of the height of the triangle is 10.4 feet.
Step-by-step explanation:
The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. Using this theorem, we can find the height of the triangle.
In this case, the base is 6 feet and the hypotenuse is 12 feet. Let's label the height as 'h'. According to the Pythagorean theorem, we have:
6^2 + h^2 = 12^2
36 + h^2 = 144
Subtracting 36 from both sides, we get:
h^2 = 108
Taking the square root of both sides, we get:
h = √108 = 10.4 feet
Therefore, the measure of the height is 10.4 feet.