In a right triangle, if one acute angle measures 30 degrees, what is the measure of the other acute angle?Choices:- 30 degrees 45 degrees 60 degrees 90 degrees
Question
In a right triangle, if one acute angle measures 30 degrees, what is the measure of the other acute angle?
Choices:
- 30 degrees
- 45 degrees
- 60 degrees
- 90 degrees
Solution
1. Break Down the Problem
In a right triangle, the sum of all angles is always 180 degrees. Since one of the angles is a right angle (90 degrees), we can use this information to find the other acute angle.
2. Relevant Concepts
The sum of the angles in a triangle can be expressed as: In a right triangle:
- One angle is (the right angle).
- Other two angles (acute angles) must sum up to .
3. Analysis and Detail
Let's denote the acute angles as:
From the properties of a right triangle: Thus:
Subtracting from both sides gives:
Now, subtract from both sides:
4. Verify and Summarize
We found that the other acute angle that complements the angle in the right triangle is .
Final Answer
The measure of the other acute angle is 60 degrees.
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