A right triangle has an acute angle measure of 22°. Which two numbers could represent the lengths of the legs of this triangle?

Refer to the right triangle below.

In the right triangle: tan(22°) = a/b
Using a calculator: tan(22°) = 0.4 = 2/5

Hence, a/b = 2/5
a : b = 2 : 5

The answer: a) 2 and 5

tan(22 degrees) is about 0.4, so the ratio of the side opposite the 22-degree angle to the side adjacent to the 22-degree angle is about 0.4, which is 2/5.  So a) is the closest.

If this was not multiple choice, I would answer that none of these are exactly right, but a) is closest.

If x,y be the lengths of the 2 legs, then
x/y=tan(22*)=0.404026225~0.4040=4040/10000=8.08/20~8/20=2/5.
Answer (a)

Math is Hard, but I'm here to help↙

????The correct answer is A.) 2 and 5. (or your first option given above)

????We will use the tangent ratio. 

????tanΘ = opposite/adjacent

tan 22° = 2/5
0.404 = 0.40

????Thus the two numbers that represent the lengths of the legs of the right triangle are 2 and 5.

The 3 angles in the right angled triangle are 90, (90-22), 22 = 90, 68, 22.;
Let hypotenuse be a = BC, opposite A. Other 2 sides are b = AC, opposite B and c = AB, opposite C. Clearly, angles (A,B,C) are (90, 68, 22);
By sine law, a/sinA = b/sinB = c/sinC, ie., a = b/sinB = c/sinC.;
Then (sinB/sinC) = (b/c) = (sin68/sin22) = 2.475086853 approx. = 2.475,;
approx = 2.5 = (5/2).;
So the 2 arms could b 2 & 5.

A right triangle has an acute angle measure of 22°. 
Which two numbers could represent the lengths of the legs of this triangle? 
a.) 2 and 5

 Acute angles measure less than 90 degrees.  This is to correct one incorrect answer.
The Three Angles of a right triangle always equal 180.   180 - 90 - 22 = 68
So the Three Angles are 90, 22 and 149.  It is impossible to solve when only three angles are given. However given your options, only A will work.