Answer:
28°
Explanation:
You want the smallest angle in a right triangle if the difference from the larger one is 34°.
Sum and difference
This is one of a class of problems in which you want to find values that have a particular sum and a particular difference. They all have the same generic solution:
- the smaller value is half the difference of the sum and difference
- the larger value is half the sum of the sum and difference
Application
Here, the sum of the two acute angles in a right triangle is 90°. The problem statement tells you their difference is 34°. That means the smaller angle is ...
smaller angle = (90° -34°)/2 = 56°/2 = 28°
The smallest angle is 28°.
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Additional comment
The largest acute angle is (90° +34°)/2 = 124°/2 = 62°. You will notice this is the complement of the 28° angle found above, and differs by ...
62° -28° = 34° . . . . as required by the problem statement
If you don't want to just jump to the answer, you can write an equation for the smallest angle (x). The larger will be (x+34).
x +(x +34) = 90 . . . . . the two acute angles are complementary
2x = 90 -34
x = (90 -34)/2 = 56/2 = 28 . . . . . this should look familiar