Oncologist use similar triangles in radiation treatment. In order to avoid creating "hot spots" on a patient's spinal cord, doctors must determine where the radiation rays will hit.The known distance from the ray to the patients back is 100 cm. The known base of the ray is 15cm. The known distance from the back to the spinal cord is 5 cm. How far apart should the doctor place the rays so they do not hit the same spot on the spinal cord?
Im confused if on what i am supposed to do
What is your subject?
Sorry I got my subjects mixed up, I meant geometry
To determine how far apart the rays should be placed, we can use the concept of similar triangles. Let's denote the distance between the rays as x cm.
First, we need to set up a proportion between the similar triangles formed by the known distances:
x / 100 = (x + 15) / 5
We can cross-multiply to solve the proportion:
5x = 100(x + 15)
5x = 100x + 1500
100x - 5x = 1500
95x = 1500
x = 1500 / 95
To calculate the value of x, we divide 1500 by 95, which gives us approximately 15.79 cm.
Therefore, the rays should be placed around 15.79 cm apart in order to avoid hitting the same spot on the patient's spinal cord.
To solve this problem, you can use the concept of similar triangles. Similar triangles have corresponding angles that are equal and their sides are proportional to each other.
Here's how you can approach this problem step by step:
Step 1: Identify the two similar triangles in this scenario.
In this case, we have two triangles: one formed by the distance from the ray to the patient's back, and the other formed by the distance from the back to the spinal cord. Let's call the first triangle "Triangle 1" and the second triangle "Triangle 2".
Step 2: Determine the corresponding sides of the two triangles.
Triangle 1 has a known base of 15 cm and a known distance from the ray to the patient's back of 100 cm.
Triangle 2 has a known distance from the back to the spinal cord of 5 cm.
Step 3: Set up a proportion using the corresponding sides of the triangles.
Since the triangles are similar, you can set up a proportion using the corresponding sides. The corresponding sides in this case are the base of Triangle 1 and the distance from the back to the spinal cord of Triangle 2.
Let 'x' represent the distance apart that the rays should be placed.
So, the proportion can be set up as:
15 cm / 100 cm = x cm / 5 cm
Step 4: Solve the proportion for 'x'.
To solve the proportion, cross-multiply and solve for 'x':
15 cm * 5 cm = 100 cm * x cm
75 cm^2 = 100 cm * x cm
Divide both sides by 100 cm:
75 cm^2 / 100 cm = x cm
0.75 cm = x cm
Therefore, the doctor should place the rays approximately 0.75 cm apart to ensure that they do not hit the same spot on the spinal cord.
Remember, in a real-life medical situation, these values may need to be adjusted based on clinical judgment and further analysis. It's always important to consult a medical professional for accurate and personalized information.