Answer:
Sample Response: You could use the Pythagorean theorem, since you know the length of the hypotenuse is 9 + 16 = 25 units and the length of one leg is 15 units. To find the value of a, use the relationship that the the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. You could also use the geometric mean (leg) theorem, which states that the length of the hypotenuse is to the length of an adjacent leg as that adjacent leg length is to the length of its corresponding segment in the hypotenuse. So you could write and solve the proportion 25/a = a/6.
Explanation:
I just did it
From the triangle given, the ways to find a will be the use of a Pythagorean theorem and a geometric mean.
By using the Pythagorean theorem, one will have to add the square of the legs and find the square root. Since the hypotenuse is 9 + 16 = 25 units and the length of one leg is 15 units. Then, in order to find the value of a, one will have to use the Pythagoras theorem.
Also, one can use the geometric mean theorem. Therefore, the values given will be rewritten as 5/a = a/6. Then, the person can solve the equation.
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