Learn Before
Finding the Unknown Angle of a Right Triangle
Apply the geometry problem-solving strategy to find the unknown acute angle in a right triangle when one acute angle is given.
Problem: One angle of a right triangle measures . What is the measure of the third angle?
- Read and draw: Sketch a right triangle and label the right angle as , the known acute angle as , and the unknown angle as .
- Identify: The measure of the third angle.
- Label: Let = the measure of the unknown angle.
- Translate: Apply the triangle angle sum property:
Substitute the known values:
- Solve: Combine the constants: . Subtract from both sides: .
- Check: →
- Answer: The measure of the third angle is .
Because a right triangle always has a angle, only one additional angle measurement is needed to determine the third. The angle sum equation reduces to , making the setup particularly straightforward.
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Learn After
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