Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°

In summary, for a right triangle with an acute angle measure of 22°, the lengths of the legs could be represented by 2 and 5, since when divided, the result is equal to the tangent of 22°. This aligns with the tangent function being used to determine the lengths of the legs. Choice a, with 2 and 5 as the lengths, is the correct answer.
  • #1
xyz_1965
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A right triangle has an acute angle measure of 22°. Which two numbers could represent the lengths of the legs of this triangle?

OPTIONS

a. 2 and 5

b. 1 and 5

c. 3 and 5

d. 4 and 5

I know that each leg represents the sides of the right triangle opposite the hypotenuse. I think the tangent function works best here.

tan(x) = opp/adj

tan(22°) = 0.4040262258

After rounding 0.4040262258 to two decimal places, I get 0.40.

I will divide the left side number by the right side number per choice given.

2/5 = 0.40

1/5 = 0.20

3/5 = 0.80

4/5 = 0.80

I say the answer is choice a.

Choice a = tan(22°).

Is this correct?
 
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  • #2
Looks good. 😁
 
  • #3
MarkFL said:
Looks good. 😁

Thank you, Mark. Check your PM here.
 

FAQ: Finding the Leg Lengths of a Right Triangle with an Acute Angle of 22°

What is a right triangle?

A right triangle is a type of triangle that has one angle measuring 90 degrees. The other two angles are acute, meaning they are less than 90 degrees.

How do you find the legs of a right triangle?

To find the legs of a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse.

Can you find the legs of a right triangle if you only know the hypotenuse?

Yes, you can use the Pythagorean theorem to find the lengths of the legs if you know the length of the hypotenuse. Rearrange the equation to solve for a or b, and then take the square root of both sides to find the length of the leg.

What if the right triangle is not a standard 3-4-5 triangle?

The Pythagorean theorem can be used for any right triangle, not just the common 3-4-5 triangle. You just need to know the lengths of two sides (the legs or the hypotenuse) to find the length of the third side.

Are there other methods for finding the legs of a right triangle?

Yes, there are other methods such as using trigonometric ratios (sine, cosine, and tangent) or the Law of Cosines. These methods may be more useful in certain situations, such as when you only know the measures of the angles in the triangle.

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