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

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To find the leg lengths of a right triangle with a 22° acute angle, the tangent function is applied, where tan(22°) equals approximately 0.40. The options provided are evaluated by dividing the lengths of the legs to see which pair yields a tangent value closest to 0.40. The calculation shows that the leg lengths of 2 and 5 (choice a) result in a tangent value of 0.40, confirming it as the correct answer. The discussion concludes with affirmation of the solution's accuracy.
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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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Looks good. 😁
 
MarkFL said:
Looks good. 😁

Thank you, Mark. Check your PM here.
 

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