The sides of a triangle are in the ratio 3:4:5. The measure of the largest angle of the triangle is

Options

A. `60^(@)`
B. `90^(@)`
C. `120^(@)`
D. `150^(@)`

Answer

To find the measure of the largest angle of a triangle with sides in the ratio 3:4:5, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the sides of the triangle**:
The sides of the triangle are in the ratio 3:4:5. We can denote the sides as:
- Side A = 3x
- Side B = 4x
- Side C = 5x
Here, x is a common multiplier.

2. **Recognize the type of triangle**:
The sides 3, 4, and 5 form a Pythagorean triplet. This means that the triangle is a right triangle.

3. **Apply the Pythagorean theorem**:
In a right triangle, the relationship between the sides is given by:
\[ a^2 + b^2 = c^2 \]
where c is the hypotenuse (the longest side). For our triangle:
\[ (3x)^2 + (4x)^2 = (5x)^2 \]
Simplifying this:
\[ 9x^2 + 16x^2 = 25x^2 \]
This confirms that the triangle is indeed a right triangle.

4. **Determine the largest angle**:
In a right triangle, the largest angle is always the right angle, which measures 90 degrees.

### Conclusion:
Thus, the measure of the largest angle of the triangle is **90 degrees**.

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