To find the angles in a triangle when given an extended ratio, we first need to understand what the ratio means. In this case, the given ratio is 3:4:8.
Let’s say the angles of the triangle are represented as:
- Angle A = 3x
- Angle B = 4x
- Angle C = 8x
Since the sum of the angles in any triangle is 180 degrees, we can set up the following equation:
3x + 4x + 8x = 180
This simplifies to:
15x = 180
Now, to find the value of x, we divide both sides by 15:
x = 180 / 15
x = 12
Now, we can find the measures of each angle by substituting x back into the expressions for each angle:
- Angle A = 3x = 3 * 12 = 36 degrees
- Angle B = 4x = 4 * 12 = 48 degrees
- Angle C = 8x = 8 * 12 = 96 degrees
Thus, the measures of the angles in the triangle are:
- Angle A = 36 degrees
- Angle B = 48 degrees
- Angle C = 96 degrees
In conclusion, when the angles in a triangle are in the ratio of 3:4:8, the angles measure 36 degrees, 48 degrees, and 96 degrees respectively.