The ratio of the angles measured of the acute angles in a right triangle is 1:2. What are the measures of these angles.
A) 30 and 60
B) 45 and 90
C) 60 and 120
D) 10 and 20
To find the measures of the acute angles in a right triangle when the ratio of the angles is given, we need to understand a few key points.
First, in any triangle, the sum of the angles is always 180 degrees.
Second, in a right triangle, one angle is always 90 degrees.
Let's use these two facts to solve the problem.
Let's assume that the measure of one of the acute angles is x degrees. According to the given ratio of 1:2, the other acute angle will be 2x degrees.
Since the sum of the three angles in any triangle is 180 degrees, we can write the equation:
x + 2x + 90 = 180
Combining like terms:
3x + 90 = 180
Subtracting 90 from both sides:
3x = 90
Dividing both sides by 3:
x = 30
Therefore, the measure of the first acute angle is 30 degrees, and the measure of the second acute angle is 2*(30) = 60 degrees.
So, the correct answer is:
A) 30 and 60