the sum of the angles in a triangle is 180 degrees. if A:B:C = 2:3:3, what is C-A?
The angles are 2x,3x,3x. The sum is 180, so x=22.5
C-A = 3x-2x = x
To find the value of C-A, we need to determine the angles corresponding to A and C first.
Step 1: Determine the total angle for the given ratio.
Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:
2x + 3x + 3x = 180
Simplifying this equation gives:
8x = 180
Step 2: Solve for x.
Dividing both sides of the equation by 8, we get:
x = 180/8
x = 22.5
Step 3: Calculate the angle measurement for A.
Multiplying x by the corresponding ratio, we find:
A = 2 * 22.5
A = 45 degrees
Step 4: Calculate the angle measurement for C.
C = 3 * 22.5
C = 67.5 degrees
Step 5: Calculate C-A.
C - A = 67.5 - 45
C - A = 22.5
Therefore, C-A is equal to 22.5 degrees.
To find the value of C-A, we first need to determine the measure of each angle in the triangle using the given ratio. Let's assume that A, B, and C represent the measures of angles A, B, and C, respectively.
Since the ratio A:B:C is given as 2:3:3, we need to find the common ratio to multiply each value.
The sum of the ratios is 2+3+3=8.
To find the measure of angle A, multiply the common ratio by the ratio assigned to A:
A = (2/8) * 180 degrees = 45 degrees.
To find the measure of angle B:
B = (3/8) * 180 degrees = 67.5 degrees.
To find the measure of angle C:
C = (3/8) * 180 degrees = 67.5 degrees.
Now that we have the measures of angles A, B, and C, we can calculate C-A:
C - A = 67.5 degrees - 45 degrees = 22.5 degrees.
Therefore, C-A is equal to 22.5 degrees.