To solve this problem, we need to determine the measures of the angles in a triangle given the ratio of the angles. The ratio provided is 3:4:5. Here’s a detailed step-by-step solution:
1. Understand the Sum of Angles in a Triangle:
In any triangle, the sum of the interior angles is always [tex]\(180^\circ\)[/tex].
2. Determine the Total Ratio:
The given ratio of the angles is 3:4:5. To find the total ratio sum:
[tex]\[
3 + 4 + 5 = 12
\][/tex]
3. Calculate Each Angle:
To find the individual angles, we can use the ratio parts and the total sum of the angles in a triangle.
- Angle 1:
[tex]\[
\text{Angle 1} = \frac{3}{12} \times 180^\circ = 45^\circ
\][/tex]
- Angle 2:
[tex]\[
\text{Angle 2} = \frac{4}{12} \times 180^\circ = 60^\circ
\][/tex]
- Angle 3:
[tex]\[
\text{Angle 3} = \frac{5}{12} \times 180^\circ = 75^\circ
\][/tex]
Therefore, the angles of the triangle, given the ratio 3:4:5, are [tex]\(45^\circ\)[/tex], [tex]\(60^\circ\)[/tex], and [tex]\(75^\circ\)[/tex].
