Question

The ratio of the angles of a triangle is $3:5:12$. Find the angle measures. Then classify the triangle by its angle measures.

Short answer

The angles measures are ${27}^{°},{45}^{°},{108}^{°}$ respectively and the triangle is a scalene triangle.

Step-by-step solution

Step 1. Given Information.

The ratio of angles of a triangle is$3:5:12$.

Step 2. Calculation.

Let the angle measures be 3x, 5x, 12x.

The sum of all the angles of a triangle is 180. Hence,

$3x+5x+12x=180°$

Adding all the x on the left side of the equation.

$20x=180°$

Divide both the sides by 20.

$\frac{20x}{20}=\frac{180°}{20}$

This will give the value of$x=9$.

Hence the angle measures are:

First angle is 3x, multiply 3 with 9.

$\begin{array}{l}3x=3\times 9\\ =27\end{array}$

Second angle 5x, multiply 5 with 9.

$\begin{array}{l}5x=5\times 9\\ =45\end{array}$

Third angle is 12x, multiply 12 with 9.

$\begin{array}{l}12x=12\times 9\\ =108\end{array}$

As all the angle measures are different, which implies that all the sides of the triangle are of different lengths. Hence the triangle is Scalene triangle.

Step 3. Conclusion.

The angle measures of the triangle are $27{}^{\circ },45{}^{\circ },108°$ and the triangle can be classified as scalene triangle.