The measure of one of the equal angles in an isoscles trinagle is twice the measure of the remaining angle. Determine the exact radian measures of the three angles in the triange
let the 'remaining' angle of the triangle be x radians
then each of the other angles is 2x radians
2x + 2x + x = pi radians
x = pi/5 radians
then the "exact" measures of the three angles are
pi/5, 2pi/5 and 2pi/5
To solve this problem, we can start by assigning variables to the angles in the triangle. Let's call the measure of one of the equal angles x, and the measure of the remaining angle y.
According to the problem statement, one of the equal angles is twice the measure of the remaining angle. This can be written as:
x = 2y
Since we know that the sum of the angles in a triangle is always 180 degrees, we can write an equation to represent this:
x + x + y = 180
Substituting the value of x from the first equation into the second equation, we get:
2y + 2y + y = 180
5y = 180
Dividing both sides by 5:
y = 36
Now we can substitute the value of y back into the first equation to find x:
x = 2y = 2(36) = 72
So the two equal angles in the triangle are each 72 degrees, and the remaining angle is 36 degrees.
To convert these angles into radian measures, we use the fact that π radians is equal to 180 degrees. So, 1 degree is equal to π/180 radians.
The radian measure of an angle is found by multiplying the degree measure by π/180.
Therefore, the two equal angles in the triangle are each 72 degrees or 72 * π/180 radians, which simplifies to 2π/5 radians.
The remaining angle is 36 degrees or 36 * π/180 radians, which simplifies to π/5 radians.
In summary, the exact radian measures of the three angles in the isosceles triangle are 2π/5 radians, 2π/5 radians, and π/5 radians.