Choose a method
Identify corresponding sides before using a similarity proportion. In a right triangle, mark the hypotenuse opposite the right angle.
Avoid this trap
Matching sides by their positions on the page can fail if a figure is rotated. For trigonometry, opposite and adjacent depend on the reference angle.
Check and transfer
A triangle has an angle sum of 180 degrees. A positive hypotenuse must exceed either leg, and sine of an acute angle lies between zero and one.
Worked example with a numerical check
Two angles in a triangle measure 34° and 48°. What is the third angle in degrees? The three interior angles sum to 180 degrees. Subtract both known angles from that total. The requested value is 98.
Contrast and diagnose
Two similar triangles have corresponding short sides 3 and 12. The smaller triangle has another side of length 7. What is the corresponding larger length? Compute the larger-to-smaller scale factor from the known corresponding sides. Multiply the requested smaller side by that factor. The requested value is 28. An incorrect approach: Multiply by the larger side instead of the side ratio.
Transfer practice
The diagram shows a right triangle. What is the length of the leg marked x? Right triangle, hypotenuse 52, one leg 20, other leg x. Try first. Check: 48. Use the Pythagorean theorem to find the square of the missing leg. Take the nonnegative square root of the hypotenuse square minus the known leg square.
Two angles in a triangle measure 34° and 48°. What is the third angle in degrees?
- The three interior angles sum to 180 degrees.
- Subtract both known angles from that total.
- The requested value is 98.
Compare the other answer choices
Report the first given angle as the missing one.
Subtract only the second angle.
Subtract only the first angle.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
Math specifications