the measures of the angles of (triangle) RST are in the ratio 2:3:5. find the measures of each, and classify the triangle as acute, right, obtuse.
2x+3x+5x = 180
10 x = 180
x = 18
2x = 36 , 3x = 54 etc
2x+3x+5x=180
10x/10=180/10
x=18
2x=2(18)=36
3x=3(18)=54
5x=5(18)=90
To find the measures of the angles in triangle RST, we need to find the actual values based on the given ratio. Let's call the measure of the smallest angle 2x, the measure of the middle angle 3x, and the measure of the largest angle 5x.
Since the sum of the angles in any triangle is always 180 degrees, we can set up an equation:
2x + 3x + 5x = 180
Simplifying the equation, we get:
10x = 180
Dividing both sides by 10, we find:
x = 18
Now, we can substitute the value of x back into the angle measures:
Smallest angle = 2x = 2 * 18 = 36 degrees
Middle angle = 3x = 3 * 18 = 54 degrees
Largest angle = 5x = 5 * 18 = 90 degrees
Now let's classify the triangle based on its angles:
Since all three angles are less than 90 degrees, we can classify this triangle as an acute triangle.