Triangle XYZ has angles measurements are in the ratio 1:3:5. What is the measurement of the largest angle?
the angle opposite the biggest side is biggest.
law of cosines
5^2 = 1^2+3^2 - 2 *1*3 cos A
However, since we don't know the sides, the law of cosines doesn't help us much.
1+3+5 = 9
180/9 = 20
so the angles are 20:60:100
The largest angle is 100°
1x+3x+5x= 180
9x = 180
x =180÷9
= 20
5×20=100
100 is the measurement of largest angle
To find the measurement of the largest angle in triangle XYZ, we need to determine the value of each angle in the ratio 1:3:5.
Let's assign variables to each angle:
Let x represent the measurement of the smallest angle.
Then, 3x represents the measurement of the second angle.
And, 5x represents the measurement of the largest angle.
Since the sum of the interior angles of a triangle is always 180 degrees, we can set up the following equation:
x + 3x + 5x = 180
Combining like terms, we have:
9x = 180
Now, let's solve for x by dividing both sides of the equation by 9:
9x/9 = 180/9
x = 20
Now that we know x is 20, we can find the measurement of the largest angle by substituting x into our expression:
5x = 5 * 20 = 100
Therefore, the measurement of the largest angle in triangle XYZ is 100 degrees.