Final answer:
To find the height of the right triangle, you can use the formula for the area and the Pythagorean theorem. The height is approximately 7.0 cm.
Step-by-step explanation:
To find the height of the triangle, we can use the formula for the area of a triangle: Area = 1/2 x base x height. Rearranging the formula, we have height = (2 x Area) / base. Plugging in the given values, we get height = (2 x 66.5 cm^2) / base. Since the triangle is a right triangle, we can use the Pythagorean theorem to find the base and then calculate the height.
Let's assume that the base is the longer side of the triangle. Using the Pythagorean theorem, we have base^2 = height^2 + (base/2)^2. Plugging in the values, we get base^2 = height^2 + (base^2)/4. Simplifying the equation, we have 3 base^2 = 4 height^2.
Now we can substitute this equation into the previous equation to find height: height = (2 x 66.5 cm^2) / (√(4 x 3)). Evaluating this expression, we get height ≈ 7.0 cm. Therefore, the height of the triangle is approximately 7.0 cm (Option A).